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On the properties (wL) and (wV)

  • Ioana Ghenciu EMAIL logo
Published/Copyright: December 30, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 6

Abstract

We characterize Banach spaces X with spaces with property (wL), i.e. spaces with the property that every L-subset of X* is weakly precompact. We prove that a Banach space X has property (wL) if and only if for any Banach space Y, any completely continuous operator T : X → Y has weakly precompact adjoint if and only if any completely continuous operator T : X → ℓ∞ has weakly precompact adjoint.

We prove that if E is a Banach space and F is a reflexive subspace of E* such that ⊥F has property (wL), then E has property (wL). We show that a space E has property RDP* (resp. the DPrcP) if and only if any closed separable subspace of E has property RDP* (resp. the DPrcP). We also show that G has property (wL) if under some conditions Kw*(E*, F) contains the dual of G.

MSC 2010: Primary 46B20; 46B28; Secondary 28B05
Keywords: the reciprocal Dunford-Pettis property; properties (wL); (wV); (V); RDP*; (wV*)

(Communicated by L’ubica Holá)

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Received: 2014-6-1
Accepted: 2015-1-5
Published Online: 2016-12-30
Published in Print: 2016-12-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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  10. Applications of extremal theorem and radius equation for a class of analytic functions
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  14. New criteria for global exponential stability of linear time-varying volterra difference equations
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  24. On the properties (wL) and (wV)
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  32. On the internal approach to differential equations 3. Infinitesimal symmetries
  34. A Characterization of the discontinuity point set of strongly separately continuous functions on products
  36. Wick differential and Poisson equations associated to the 𝚀𝚆𝙽-Euler operator acting on generalized operators
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  40. On codes over 𝓡k, m and constructions for new binary self-dual codes
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https://doi.org/10.1515/ms-2016-0232
Keywords for this article
the reciprocal Dunford-Pettis property; properties (wL); (wV); (V); RDP*; (wV*)

Articles in the same Issue

  2. A triple representation of lattice effect algebras
  4. Periods of morgan-voyce sequences and elliptic curves
  6. Multiplicative generalized derivations on ideals in semiprime rings
  8. A few remarks on Poincaré-Perron solutions and regularly varying solutions
  10. Applications of extremal theorem and radius equation for a class of analytic functions
  12. On the “bang-bang” principle for a class of Riemann-Liouville fractional semilinear evolution inclusions
  14. New criteria for global exponential stability of linear time-varying volterra difference equations
  16. On approximation of functions by some hump matrix means of Fourier series
  18. Pseudo-amenability and pseudo-contractibility for certain products of Banach algebras
  20. Poisson kernels on semi-direct products of abelian groups
  22. Locally convex projective limit cones
  24. On the properties (wL) and (wV)
  26. On the existence of solutions for quadratic integral equations in Orlicz spaces
  28. Existence and uniqueness of best proximity points under rational contractivity conditions
  30. Almost Weyl structures on null geometry in indefinite Kenmotsu manifolds
  32. On the internal approach to differential equations 3. Infinitesimal symmetries
  34. A Characterization of the discontinuity point set of strongly separately continuous functions on products
  36. Wick differential and Poisson equations associated to the 𝚀𝚆𝙽-Euler operator acting on generalized operators
  38. Multivariate EIV models
  40. On codes over 𝓡k, m and constructions for new binary self-dual codes
  42. Domination number of total graphs
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