Generalizations of Reid inequality
-
Abstract
In this paper, we improve the famous Reid inequality related to linear operators. Some monotony results for positive operators are also established with a different approach from what is known in the existing literature. Lastly, Reid’s (and Halmos-Reid’s) inequalities are extended to unbounded operators.
(Communicated by Werner Timmermann)
Acknowledgement
We warmly thank Professor J. Stochel for communicating Lemma 2.4 to the corresponding author.
We also thank the anonymous referees for all their suggestions and valuable remarks.
References
[1] Dehimi, S.—Mortad, M. H.: Right (or left) invertibility of bounded and unbounded operators and applications to the spectrum of products, Complex Anal. Oper. Theory 12(3) (2018), 589–597. 10.1007/s11785-017-0687-z.Suche in Google Scholar
[2] Halmos, P. R.: A Hilbert Space Problem Book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967.Suche in Google Scholar
[3] Kato, T.: Perturbation Theory for Linear Operators, 2nd edition, Springer, 1980.Suche in Google Scholar
[4] Kittaneh, F.: Notes on some inequalities for Hilbert space operators, Publ. Res. Inst. Math. Sci. 24(2) (1988), 283–293.10.2977/prims/1195175202Suche in Google Scholar
[5] Lin, C.-S.: Inequalities of Reid type and Furuta, Proc. Amer. Math. Soc. 129(3) (2001), 855–859.10.1090/S0002-9939-00-05650-1Suche in Google Scholar
[6] Lin, C.-S.—Dragomir, S. S.: On high-power operator inequalities and spectral radii of operators, Publ. Res. Inst. Math. Sci. 42(2) (2006), 391–397.10.2977/prims/1166642108Suche in Google Scholar
[7] Mortad, M. H.: An improvement of Reid inequality, arXiv:1704.05104v1.Suche in Google Scholar
[8] Reid, W. T.: Symmetrizable completely continuous linear transformations in Hilbert space, Duke Math. J. 18 (1951), 41–56.10.1215/S0012-7094-51-01805-4Suche in Google Scholar
[9] Schmüdgen, K.: Unbounded Self-Adjoint Operators on Hilbert Space. Springer GTM 265, 2012.10.1007/978-94-007-4753-1Suche in Google Scholar
[10] Young, N.: An Introduction to Hilbert Space. Cambridge Mathematical Textbooks, Cambridge University Press, Cambridge, 1988.Suche in Google Scholar
© 2018 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Idempotents, group membership and their applications
- Residuation in non-associative MV-algebras
- An extension of F. Šik’s theorem on modular lattices
- Weak pseudo-BCK algebras
- Witt functor of a quadratic order
- A modification of a problem of Diophantus
- Cauchy problems involving a Hadamard-type fractional derivative
- Caratheodory’s solution of the Cauchy problem and a question of Z. Grande
- Sturm-Picone comparison theorems for nonlinear impulsive differential equations
- On oscillatory fourth order nonlinear neutral differential equations – III
- Local-periodic solutions for functional dynamic equations with infinite delay on changing-periodic time scales
- On the representation of involutive Jamesian functions
- Refinements of the heinz inequalities for operators and matrices
- Generalizations of Reid inequality
- Probabilistic convergence transformation groups
- Cluster sets and topology
- Some characterizations for Markov processes as mixed renewal processes
- Equivalent conditions of complete convergence for weighted sums of ANA random variables
Artikel in diesem Heft
- Idempotents, group membership and their applications
- Residuation in non-associative MV-algebras
- An extension of F. Šik’s theorem on modular lattices
- Weak pseudo-BCK algebras
- Witt functor of a quadratic order
- A modification of a problem of Diophantus
- Cauchy problems involving a Hadamard-type fractional derivative
- Caratheodory’s solution of the Cauchy problem and a question of Z. Grande
- Sturm-Picone comparison theorems for nonlinear impulsive differential equations
- On oscillatory fourth order nonlinear neutral differential equations – III
- Local-periodic solutions for functional dynamic equations with infinite delay on changing-periodic time scales
- On the representation of involutive Jamesian functions
- Refinements of the heinz inequalities for operators and matrices
- Generalizations of Reid inequality
- Probabilistic convergence transformation groups
- Cluster sets and topology
- Some characterizations for Markov processes as mixed renewal processes
- Equivalent conditions of complete convergence for weighted sums of ANA random variables
