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Some results on disjointly weakly compact sets

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Veröffentlicht/Copyright: 29. September 2025
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Demonstratio Mathematica
Aus der Zeitschrift Demonstratio Mathematica Band 58 Heft 1

Abstract

We give an operator characterization of disjointly weakly compact sets and show that disjointly weakly compact sets coincide with reciprocal Dunford-Pettis sets. We compare disjointly weakly compact sets with almost Grothendieck sets, relatively compact sets, and weak reciprocal Dunford-Pettis sets. Consequently, we obtain new characterizations of the weak Grothendieck property, Schur property, and Banach lattices whose dual have an order continuous norm.

Keywords: disjointly weakly compact set; reciprocal Dunford-Pettis set; almost Grothendieck set; Banach lattice; order continuous norm
MSC 2010: 46B42; 46B50; 46B40

1 Introduction and preliminaries

Throughout this article, all spaces will be assumed to be nonzero real Banach spaces or Banach lattices. We denote arbitrary Banach spaces by X and Y , and Banach lattices by E . By B X , we denote the closed unit ball of X . The symbol X ′ stands for the norm dual of X . By a bounded set, we mean a norm bounded set. The positive cone of a Banach lattice is denoted by E + , that is, E + = { x ∈ E : x ≥ 0 } . For any x ∈ E , the positive part, the negative part, and the modulus of x are denoted by x + , x − , and ∣ x ∣ , respectively. In a Banach lattice E , the order interval from x to y is given by [ x , y ] = { z ∈ E : x ≤ z ≤ y } . We denote the solid hull of a set A ⊆ E by Sol ( A ) , which is the smallest solid set containing A . An operator T from X into Y is denoted by T : X → Y . In this work, all operators are assumed to be linear and bounded. If T : X → Y is an operator, the adjoint operator of T is defined as T ′ : Y ′ → X ′ , ( T ′ f ) ( x ) = f ( T x ) for each f ∈ Y ′ and for each x ∈ X .

Disjointly weakly compact sets were introduced by Wnuk in [1]. We recall that a bounded subset A of E is called disjointly weakly compact if every disjoint sequence in Sol ( A ) converges weakly to zero. In a Banach lattice E , the closed unit ball B E is disjointly weakly compact if and only if E ′ has an order continuous norm [2, Theorem 2.4.14]. As indicated in [3], disjointly weakly compact sets are weak versions of L-weakly compact sets. There is a broad literature on L-weakly compact sets, but disjointly weakly compact sets have been studied in detail only recently [3–5]. In [3], among other things, the authors have established some characterizations of disjointly weakly compact sets. They have also investigated its relationship with relatively weakly compact sets, L-weakly compact sets, almost Dunford-Pettis sets, and almost limited sets. As a result, they have obtained some characterizations of well-known Banach lattice properties such as Kantorovich-Banach space, positive Schur property, and weak Dunford-Pettis property. The connection between disjointly weakly compact sets with weakly precompact sets and positively limited sets have been given in [4] and [5], respectively.

In Banach space theory, various sets have been defined or characterized by using operators. These include Dunford-Pettis sets, reciprocal Dunford-Pettis sets, limited sets, weakly precompact sets, and Grothendieck sets. In Banach lattice theory, disjoint versions of some of these sets have also been studied [6–8]. Almost Grothendieck sets have been recently introduced in [6]. We recall that a subset A ⊆ E is called an almost Grothendieck set if T ( A ) is relatively weakly compact in c 0 for every disjoint operator T : E → c 0 [6]. The class of almost Grothendieck sets is a disjoint version of that of Grothendieck sets, and it characterizes the weak Grothendieck property [6, Proposition 2.2]. Another class of sets that is defined by using operators into c 0 is that of weak reciprocal Dunford-Pettis sets [9]. A bounded set A ⊆ X is called a weak reciprocal Dunford-Pettis set if T ( A ) is relatively weakly compact for each Dunford-Pettis (or completely continuous) operator T : E → c 0 [9].

In this article, we study disjointly weakly compact sets and some of their properties. We first give an operator characterization of disjointly weakly compact sets. We show that disjointly weakly compact sets and reciprocal Dunford-Pettis sets coincide in Banach lattices. We investigate the relationship between disjointly weakly compact sets and almost Grothendieck sets. As a result, we obtain new characterizations of the weak Grothendieck property and Banach lattices whose duals have order continuous norm. By giving the relationship between relatively compact sets and disjointly weakly compact sets, we obtain a characterization of the Schur property. Finally, we investigate when weak reciprocal Dunford-Pettis sets coincide with disjointly weakly compact sets.

Let us recall some definitions. A Banach lattice E is said to have an order continuous norm if for each net ( x α ) in E satisfying x α ↓ 0 , we have ∥ x α ∥ → 0 . Here, x α ↓ 0 means that the net ( x α ) is decreasing, its infimum exists, and inf ( x α ) = 0 . A bounded subset A ⊆ E is called L-weakly compact if every disjoint sequence in sol ( A ) converges to zero in norm. It is known that L-weakly compact sets are relatively weakly compact, but not necessarily compact. A bounded subset A of a Banach space X is called a reciprocal Dunford-Pettis set if T ( A ) is relatively weakly compact for each Dunford-Pettis (or completely continuous) operator T with domain X [9,10]. A Banach space is said to have the Schur property if weakly convergent sequences are convergent in norm. This condition holds if and only if every relatively weakly compact set is relatively compact. For instance, the sequence space l 1 has the Schur property. A Banach lattice E is said to have the weak Grothendieck property if every disjoint weak* null sequence in E ′ is weakly null [6,11]. This property is weaker than the Grothendieck property. For instance, l 1 has the weak Grothendieck property but not the Grothendieck property [11, p. 768]. An operator T : X → Y is called a Dunford-Pettis (or completely continuous) operator if for each weakly null sequence ( x n ) in X , we have ∥ T x n ∥ → 0 . The class of almost Dunford-Pettis operators was introduced in [12] and has been studied by many authors [12–16]. An operator T : E → Y is called almost Dunford-Pettis if ∥ T x n ∥ → 0 for each disjoint weakly null sequence ( x n ) in E . Clearly, each Dunford-Pettis operator defined on a Banach lattice is almost Dunford-Pettis. If T : E → c 0 is an operator, then there exists a unique weak* null sequence ( f n ) in E ′ such that T x = ( f n ( x ) ) for all x ∈ E . Then, T is called a disjoint operator whenever ( f n ) is a disjoint sequence in E ′ [6, p. 2]. We refer to [1,2,17] for any unexplained notation and terminology.

2 Main results

For our first result, we will need the following Lemma 1 [17, Theorem 5.63].

Lemma 1

Let E be a Banach lattice, A ⊆ E and B ⊆ E ′ be bounded sets. Then the following assertions are equivalent.

  1. Every disjoint sequence in sol ( A ) converges uniformly to zero on B.

  2. Every disjoint sequence in sol ( B ) converges uniformly to zero on A.

We begin by giving an operator characterization of disjointly weakly compact sets.

Theorem 1

Let A be a bounded subset of a Banach lattice E. Then the following statements are equivalent.

  1. The set A is disjointly weakly compact.

  2. For each disjoint sequence ( x n ) in sol ( A ) and for each almost Dunford-Pettis operator T : E → Y , we have ∥ T x n ∥ → 0 for each Banach space Y.

  3. For each disjoint sequence ( x n ) in sol ( A ) and for each Dunford-Pettis operator T : E → Y , we have ∥ T x n ∥ → 0 for each Banach space Y.

  4. For each disjoint sequence ( x n ) in sol ( A ) and for each Dunford-Pettis operator T : E → c 0 , we have ∥ T x n ∥ → 0 .

Proof

( i ⇒ i i ) Let ( x n ) be a disjoint sequence in sol ( A ) and assume that T : E → Y is an almost Dunford-Pettis operator, where Y is an arbitrary Banach space. Since A is disjointly weakly compact, we have x n → w 0 . This implies that ∥ T x n ∥ → 0 .

( i i ⇒ i i i ) Obvious.

( i i i ⇒ i v ) Obvious.

( i v ⇒ i ) Let ( f n ) be a disjoint L-sequence in E ′ . By [3, Theorem 2.3(3)], we need to show that ( f n ) converges uniformly to zero on A . We define T : E ⟶ c 0 by

(1) T x = ( f n ( x ) ) .

Since ( f n ) is a disjoint L-sequence, it converges to zero in σ ( E ′ , E ) [3, p. 3]. This means that f n ( x ) → 0 for all x ∈ E . Thus, T takes values in c 0 . To show that T is a Dunford-Pettis operator, we take a weakly null sequence ( x n ) in E . Since B ≔ { f n : n ∈ N } is an L-set, ( x n ) converges uniformly to zero on B , that is,

(2) ∥ T x n ∥ = sup i ∣ f i ( x n ) ∣ → 0 .

Hence, T is a Dunford-Pettis operator. By the assumption and from equation (2), we see that each disjoint sequence in sol ( A ) converges uniformly to zero on B . According to Lemma 1 [17, Theorem 5.63], each disjoint sequence in sol ( B ) , and in particular ( f n ) , converges uniformly to zero on A . Thus, A is a disjointly weakly compact set.□

In the following result, we prove that disjointly weakly compact sets and reciprocal Dunford-Pettis sets coincide in Banach lattices.

Theorem 2

Let E be a Banach lattice and A ⊆ E be a bounded set. Then the following assertions are equivalent.

  1. The set A is disjointly weakly compact.

  2. For each Dunford-Pettis operator T : E → Y , the set T ( A ) is relatively weakly compact for each Banach space Y, that is, A is a reciprocal Dunford-Pettis set.

Proof

Assume that A is a disjointly weakly compact set. Let T : E → Y be a Dunford-Pettis operator, where Y is an arbitrary Banach space. Put C ≔ sol ( A ) . By Theorem 1, ∥ T x n ∥ → 0 for each disjoint sequence ( x n ) ⊆ C . It follows from [17, Theorem 4.36] that for all ε > 0 , there exists some u ε ∈ E + so that

(3) ∥ T ( ∣ x ∣ − u ε ) + ∥ < ε

holds for all x ∈ C . The lattice identity ∣ x ∣ = ∣ x ∣ ∧ u + ( ∣ x ∣ − u ) + yields that

(4) T ( C + ) ⊆ T [ − u , u ] + ε B Y .

Since T is a Dunford-Pettis operator, it sends each order interval into a relatively weakly compact set. Hence, the set T [ − u , u ] is relatively weakly compact. This implies that T ( C + ) is also relatively weakly compact ([1, Theorem A.14] or [17, Theorem 3.44]). From C ⊆ C + − C + , we conclude that T ( C ) is relatively weakly compact, and so is T ( A ) .

Now we assume that the condition in (ii) holds. To show that A is a disjointly weakly compact set, let ( f n ) be an order bounded disjoint sequence in E ′ [3, Theorem 2.3(4)]. Here, we may assume that 0 ≤ f n ≤ f for some f ∈ E ′ . We define S : E → l 1 by

(5) S x = ( f n ( x ) ) .

Since ( f n ) is order bounded and disjoint, we have

(6) ∑ n = 1 k ∣ f n ( x ) ∣ ≤ ∑ n = 1 k f n ( ∣ x ∣ ) ≤ f ( ∣ x ∣ ) < ∞ .

Therefore, S takes values in l 1 . Since l 1 has the Schur property, S is a Dunford-Pettis operator. By the assumption, the set S ( A ) is relatively weakly compact. The Schur property of l 1 yields that S ( A ) is relatively compact. By the characterization of relatively compact (or norm totally bounded) sets in l 1 [17, Theorem 4.33], for each ε > 0 , there exists some n ε ∈ N such that

(7) f n ( x ) ≤ ∑ i = n ε ∞ ∣ f i ( x ) ∣ < ε

holds for each n ≥ n ε and for each x ∈ A . This shows that sup x ∈ A ∣ f n ( x ) ∣ → 0 . Hence, A is disjointly weakly compact.□

In general, disjointly weakly compact sets are not almost Grothendieck, and vice versa. For example, B l 1 is an almost Grothendieck set [6, p. 3], but not a disjointly weakly compact set. On the other hand, B c 0 is disjointly weakly compact, but not almost Grothendieck [6, p. 3]. Below we give a necessary and sufficient condition which insures that each disjointly weakly compact set is almost Grothendieck. Recall that, if E has an order unit u , then E is an abstract M-space (AM-space) with unit, and [ − u , u ] is the closed unit ball of E [17, p. 195].

Proposition 1

Let E be a Banach lattice with an order unit. Then the following statements are equivalent.

  1. E has the weak Grothendieck property.

  2. Each disjointly weakly compact set in E is almost Grothendieck.

Proof

( i ⇒ i i ) Follows from [6, Proposition 2.2].

( i i ⇒ i ) Let ( f n ) be a disjoint weak* null sequence in E ′ . We will show that f n → w 0 . We define T : E ⟶ c 0 as in Theorem 1. Thus, T is a disjoint operator. Let u ∈ E + be the order unit of E . Since order intervals are disjointly weakly compact, [ − u , u ] is a disjointly weakly compact set. By the hypothesis, [ − u , u ] is an almost Grothendieck set. Thus, T [ − u , u ] is a relatively weakly compact set in c 0 . It follows that the operator T : E ⟶ c 0 is weakly compact. The adjoint operator T ′ : l 1 ⟶ E ′ is given by

(8) T ′ ( α n ) = ∑ n = 1 ∞ α n f n ,

and T ′ is also weakly compact by Gantmacher’s Theorem. Hence, T ′ ( B l 1 ) is a relatively weakly compact set. Since T ′ ( e n ) = f n holds, the set { f n : n ∈ N } is also relatively weakly compact. The disjointness of the sequence ( f n ) implies that f n → w 0 [17, Theorem 4.34].□

Now we consider the case when each almost Grothendieck set is disjointly weakly compact.

Proposition 2

Let E be a Banach lattice. The norm of E ′ is order continuous if and only if each almost Grothendieck set in E is disjointly weakly compact.

Proof

If the norm of E ′ is order continuous, then B E is disjointly weakly compact, and hence, each almost Grothendieck set is disjointly weakly compact. For the converse, suppose that the norm of E ′ is not order continuous. By [17, Theorem 4.69(1)], l 1 is lattice embeddable in E . So there exists a lattice embedding S : l 1 ⟶ E . Put x n ≔ S ( e n ) . Then ( x n ) is a disjoint sequence in E . Since the closed unit ball of l 1 is almost Grothendieck, the set { x n : n ∈ N } is almost Grothendieck, and hence disjointly weakly compact by the hypothesis. Thus, x n → w 0 . But this is a contradiction, since a weakly null sequence in a Banach space cannot be equivalent to the standard basis of l 1 [17, p. 248].□

It is obvious that each relatively compact set is disjointly weakly compact. We give a necessary and sufficient condition which forces that each disjointly weakly compact set is relatively compact.

Proposition 3

Let E be a Banach lattice. Then E has the Schur property if and only if each disjointly weakly compact set in E is relatively compact.

Proof

Assume that E has the Schur property. Let A ⊆ E be a disjointly weakly compact set. It is sufficient to show that A is relatively weakly compact. Let ( x n ) be a disjoint sequence in sol ( A ) . Then x n → w 0 . By the Schur property, we have ∥ x n ∥ → 0 . Therefore, A is L-weakly compact, and hence relatively weakly compact. The converse is obvious.□

The class of weak reciprocal Dunford-Pettis sets was introduced in [9]. From Theorem 2, it is clear that in Banach lattices each disjointly weakly compact set is a weak reciprocal Dunford-Pettis set. If the norm dual E ′ has an order continuous norm, then the converse also holds. We show that this condition is also necessary if we assume that each weak* null L-sequence in E ′ is weakly null.

Proposition 4

Let E be a Banach lattice such that for each weak* null L-sequence ( f n ) ⊆ E ′ , we have f n → w 0 . If each weak reciprocal Dunford-Pettis set in E is disjointly weakly compact, then E ′ has an order continuous norm.

Proof

Let ( x n ) ⊆ E be a norm bounded disjoint sequence. Put A ≔ { x n : n ∈ N } . Let T : E → c 0 be a Dunford-Pettis operator. Then there exists a weak* null sequence ( g n ) ⊆ E ′ such that T x = ( g n ( x ) ) holds for each x ∈ E . Since T is a Dunford-pettis operator, ( g n ) is an L-sequence. By our assumption, g n → w 0 . Therefore, T is a weakly compact operator [17, Theorem 5.26]. This implies that A is a weak reciprocal Dunford-Pettis set. Hence, A is disjointly weakly compact by the hypothesis. Thus, x n → w 0 . Consequently, the norm of E ′ is order continuous [1, Theorem 3.1]□

Acknowledgments

The authors would like to thank the reviewers for their careful reading of the manuscript and valuable comments.

  1. Funding information: Authors state no funding involved.

  2. Author contributions: Both authors have accepted responsibility for the entire content of this manuscript and approved its submission to the journal.

  3. Conflict of interest: The authors state no conflict of interest.

  4. Data availability statement: Not applicable.

References

[1] W. Wnuk, Banach lattices with order continuous norms, Polish Scientific Publishers PWN, Warszawa, 1999. Suche in Google Scholar

[2] P. Meyer-Nieberg, Banach Lattices, Springer-Verlag, Berlin, 1991. 10.1007/978-3-642-76724-1Suche in Google Scholar

[3] B. Xiang, J. X. Chen, L. Li, Disjointly weak compactness in Banach lattices, Positivity 27 (2023), no. 5, 58. 10.1007/s11117-023-01012-5Suche in Google Scholar

[4] B. Xiang, J. X. Chen, and L. Li, Weak precompactness in Banach lattices, Positivity 26 (2022), no. 1, 4. 10.1007/s11117-022-00873-6Suche in Google Scholar

[5] H. Ardakani and J. X. Chen, Positively limited sets in Banach lattices, J. Math. Anal. Appl. 526 (2023), no. 1, 127220. 10.1016/j.jmaa.2023.127220Suche in Google Scholar

[6] P. Galindo, V. C. C. Miranda, Grothendieck-type subsets of Banach lattices, J. Math. Anal. Appl. 506 (2022), no. 1, 125570. 10.1016/j.jmaa.2021.125570Suche in Google Scholar

[7] J. X. Chen, Z. L. Chen, G. X. Ji, Almost limited sets in Banach lattices, J. Math. Anal. Appl. 412 (2014), no. 1, 547–553. 10.1016/j.jmaa.2013.10.085Suche in Google Scholar

[8] K. Bouras, Almost Dunford-Pettis sets in Banach lattices, Rend. Circ. Mat. Palermo 62 (2013), 227–236. 10.1007/s12215-013-0105-ySuche in Google Scholar

[9] I Ghenciu, A note on weak reciprocal Dunford-Pettis sets, Acta Math. Hungar. 152 (2017), no. 2, 453–463. 10.1007/s10474-017-0723-5Suche in Google Scholar

[10] E. Bator, P. Lewis, and J. Ochoa, Evaluation maps, restriction maps, and compactness, Colloq. Math. 78 (1998), no. 1, 1–17. 10.4064/cm-78-1-1-17Suche in Google Scholar

[11] N. Machrafi, K. E. Fahri, M. Moussa, and B. Altin, A note on weak almost limited operators, Hacet. J. Math. Stat. 48 (2019), no. 3, 759–770. 10.15672/HJMS.2018.550Suche in Google Scholar

[12] J. A. Sanchez, Operators on Banach Lattices, Ph.D. Thesis, Complutense University, Madrid, 1985. Suche in Google Scholar

[13] W. Wnuk, Banach lattices with the weak Dunford-Pettis property, Atti Sem. Mat. Fis. Univ. Modena 42 (1994), 227–236. Suche in Google Scholar

[14] B. Aqzzouz, A. Elbour, and A. W. Wickstead, Positive almost Dunford-Pettis operators and their duality, Positivity 15 (2011), no. 2, 185–197. 10.1007/s11117-010-0050-3Suche in Google Scholar

[15] B. Aqzzouz and A. Elbour, Some characterizations of almost Dunford-Pettis operators and applications, Positivity 15 (2011), no. 3, 369–380. 10.1007/s11117-010-0083-7Suche in Google Scholar

[16] B. Aqzzouz and A. Elbour, Semi-compactness of almost Dunford-Pettis operators on Banach lattices, Demonstr. Math. 44 (2011), no. 1, 131–141. 10.1515/dema-2013-0287Suche in Google Scholar

[17] C. D. Aliprantis and O. Burkinshaw, Positive Operators, Springer, Dordrecht, 2006. 10.1007/978-1-4020-5008-4Suche in Google Scholar
Received: 2024-01-12
Revised: 2024-11-04
Accepted: 2025-08-19
Published Online: 2025-09-29

© 2025 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/dema-2025-0169
Schlagwörter für diesen Artikel
disjointly weakly compact set; reciprocal Dunford-Pettis set; almost Grothendieck set; Banach lattice; order continuous norm
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  30. Solutions of several general quadratic partial differential-difference equations in ℂ2
  31. Inequalities for the generalized trigonometric functions with respect to weighted power mean
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  38. Behavior of spatial curves under different transformations in Euclidean 4-space
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  42. On the approximation of Kantorovich-type Szàsz-Charlier operators
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  46. Review Article
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  48. Special Issue on Differential Equations and Numerical Analysis - Part II
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  64. Special Issue on Blow-up Phenomena in Nonlinear Equations of Mathematical Physics - Part II
  65. Energy decay of a coupled system involving a biharmonic Schrödinger equation with an internal fractional damping
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  67. Nonlinear heat equation with viscoelastic term: Global existence and blowup in finite time
  68. New Jensen's bounds for HA-convex mappings with applications to Shannon entropy
  69. Special Issue on Approximation Theory and Special Functions 2024 conference
  70. Ulam-type stability for Caputo-type fractional delay differential equations
  71. Faster approximation to multivariate functions by combined Bernstein-Taylor operators
  72. (λ, ψ)-Bernstein-Kantorovich operators
  73. Some special functions and cylindrical diffusion equation on α-time scale
  74. (q, p)-Mixing Bloch maps
  75. Orthogonalizing q-Bernoulli polynomials
  76. On better approximation order for the max-product Meyer-König and Zeller operator
  77. Moment-based approximation for a renewal reward process with generalized gamma-distributed interference of chance
  78. A note on linear compositions of the Mellin convolution operators in the weighted Mellin-Lebesgue spaces
  79. A new perspective on generalized Laguerre polynomials
  80. Global existence of semilinear system of Klein-Gordon equations in anti-de Sitter spacetime
  81. Estimates for Durrmeyer-type exponential sampling series in Mellin-Orlicz spaces
  82. Special Issue on Variational Methods and Nonlinear PDEs
  83. A note on mean field type equations
  84. Ground states for fractional Kirchhoff double-phase problem with logarithmic nonlinearity
  85. Solution of nonlinear Langevin equations involving Hilfer-Hadamard fractional order derivatives and variable coefficients
  86. Bifurcation, quasi-periodic, and wave solutions to the fractional model of optical fibers in communication systems
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Heruntergeladen am 1.10.2025 von https://www.degruyterbrill.com/document/doi/10.1515/dema-2025-0169/html
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