Numerical Radius Inequalities for Hilbert Space Operators

By Mohammad Wajeeh Alomari. Complex Analysis and Operator Theory, 2018

351 citations recorded by the source corpus.

In this work, an improvement of Hölder–McCarty inequality is established. Based on that, several refinements of the generalized mixed Schwarz inequality are obtained. Consequently, some new numerical radius inequalities are proved. New inequalities for numerical radius of n×n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\times n$$\end{document} matrix of Hilbert space operators are proved as well. Some refinements of some earlier results were proved in literature are also given. Some of the presented results are refined and it shown to be better than earlier results were proved in literature.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c55d8b788c4d40b40c5121cd13dda5f057b1046b

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Citations in the corpus

More accurate numerical radius inequalities (I) (2019, positive): “In [5], Kittaneh proved that for any A ∈ B(H), w2(A) ≤ 1 2 ∥∥∥|A|2 + ∣∣A∗∣∣2∥∥∥ .”
Development of inequalities and characterization of equality conditions for the numerical radius (2021, methodology): “In this paper, we obtain lower bounds for the numerical radius of bounded linear operators which reﬁne the well known lower bound w ( A ) ≥ A 2 and the bound w 2 ( A ) ≥ A ∗ A + AA ∗ , obtained by Kittaneh [12, Th. 1].”
Bounds of numerical radius of bounded linear operators using t-Aluthge transform (2019, background): “Various mathematicians [2, 3, 4, 7, 8, 11, 12, 13] have studied and improved on the numerical radius inequality over the years using diﬀerent techniques.”
Numerical radius inequalities and its applications in estimation of zeros of polynomials (2019, background): “Various numerical radius inequalities improving this inequality have been given in [4, 6, 12, 13, 17].”
Power Inequalities for the Numerical Radius of a Product of Two Operators in Hilbert Spaces (2024, background): “For recent inequalities involving the numerical radius, see [1] -[9], [13], [14]-[16] and [17].”
Some improvements of numerical radius inequalities of operators and operator matrices (2019, background): “2 PINTU BHUNIA AND KALLOL PAUL Various numerical radius inequalities improving this inequality have been given in [3, 4, 6, 7, 9, 10, 11, 13, 14, 16, 19, 20, 21, 22].”
A note on the A-numerical radius of operators in semi-Hilbert spaces (2020, background): “If A = I, we get the classical numerical radius (see [5,8,9]).”
On inequalities for A-numerical radius of operators (2019, background): “ON INEQUALITIES FOR A-NUMERICAL RADIUS OF OPERATORS 3 Over the years many mathematicians have studied numerical radius inequalities in [5, 7, 8, 9, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24].”