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Search Results (3)

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Keywords = Euclidean operator A-seminorm

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15 pages, 303 KB  
Article
New Results on Boas–Bellman-Type Inequalities in Semi-Hilbert Spaces with Applications
by Najla Altwaijry, Silvestru Sever Dragomir and Kais Feki
Axioms 2023, 12(7), 638; https://doi.org/10.3390/axioms12070638 - 27 Jun 2023
Cited by 2 | Viewed by 1570
Abstract
In this article, we investigate new findings on Boas–Bellman-type inequalities in semi-Hilbert spaces. These spaces are generated by semi-inner products induced by positive and positive semidefinite operators. Our objective is to reveal significant properties of such spaces and apply these results to the [...] Read more.
In this article, we investigate new findings on Boas–Bellman-type inequalities in semi-Hilbert spaces. These spaces are generated by semi-inner products induced by positive and positive semidefinite operators. Our objective is to reveal significant properties of such spaces and apply these results to the field of multivariable operator theory. Specifically, we derive new inequalities that relate to the joint A-numerical radius, the joint operator A-seminorm, and the Euclidean A-seminorm of tuples of semi-Hilbert space operators. We assume that A is a nonzero positive operator. Our discoveries provide insights into the structure of semi-Hilbert spaces and have implications for a broad range of mathematical applications and beyond. Full article
(This article belongs to the Special Issue Operator Theory and Its Applications II)
18 pages, 336 KB  
Article
On the Joint A-Numerical Radius of Operators and Related Inequalities
by Najla Altwaijry, Silvestru Sever Dragomir and Kais Feki
Mathematics 2023, 11(10), 2293; https://doi.org/10.3390/math11102293 - 15 May 2023
Cited by 4 | Viewed by 1983
Abstract
In this paper, we study p-tuples of bounded linear operators on a complex Hilbert space with adjoint operators defined with respect to a non-zero positive operator A. Our main objective is to investigate the joint A-numerical radius of the p [...] Read more.
In this paper, we study p-tuples of bounded linear operators on a complex Hilbert space with adjoint operators defined with respect to a non-zero positive operator A. Our main objective is to investigate the joint A-numerical radius of the p-tuple.We established several upper bounds for it, some of which extend and improve upon a previous work of the second author. Additionally, we provide several sharp inequalities involving the classical A-numerical radius and the A-seminorm of semi-Hilbert space operators as applications of our results. Full article
(This article belongs to the Special Issue Dynamical Systems and Operator Theory)
20 pages, 333 KB  
Article
Inequalities and Reverse Inequalities for the Joint A-Numerical Radius of Operators
by Najla Altwaijry, Silvestru Sever Dragomir and Kais Feki
Axioms 2023, 12(3), 316; https://doi.org/10.3390/axioms12030316 - 22 Mar 2023
Viewed by 2191
Abstract
In this paper, we aim to establish several estimates concerning the generalized Euclidean operator radius of d-tuples of A-bounded linear operators acting on a complex Hilbert space H, which leads to the special case of the well-known A-numerical radius [...] Read more.
In this paper, we aim to establish several estimates concerning the generalized Euclidean operator radius of d-tuples of A-bounded linear operators acting on a complex Hilbert space H, which leads to the special case of the well-known A-numerical radius for d=1. Here, A is a positive operator on H. Some inequalities related to the Euclidean operator A-seminorm of d-tuples of A-bounded operators are proved. In addition, under appropriate conditions, several reverse bounds for the A-numerical radius in single and multivariable settings are also stated. Full article
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