Generalizations of Reid inequality
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Souheyb Dehimi
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
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© 2018 Mathematical Institute Slovak Academy of Sciences
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- On the representation of involutive Jamesian functions
- Refinements of the heinz inequalities for operators and matrices
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Articles in the same Issue
- 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
