June 2023 NUMERICAL RADIUS INEQUALITIES VIA TRIANGLE-TYPE INEQUALITIES
Badria Timroi, Mohsen Erfanian Omidvar
Rocky Mountain J. Math. 53(3): 951-958 (June 2023). DOI: 10.1216/rmj.2023.53.951

Abstract

Several upper estimates for the numerical radius of Hilbert space operators are given. For a bounded linear operator T on a complex Hilbert space and 0α1, with the polar decomposition T=U|T|, it is shown that

ω(T)12T+14(|T|2α+|T|2(1α)+ω(T~α)),

where T~α=|T|αU|T|1α is the generalized Aluthge transformation of T. Related norm inequalities are also obtained.

Citation

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Badria Timroi. Mohsen Erfanian Omidvar. "NUMERICAL RADIUS INEQUALITIES VIA TRIANGLE-TYPE INEQUALITIES." Rocky Mountain J. Math. 53 (3) 951 - 958, June 2023. https://doi.org/10.1216/rmj.2023.53.951

Information

Received: 5 October 2021; Revised: 29 June 2022; Accepted: 5 July 2022; Published: June 2023
First available in Project Euclid: 21 July 2023

MathSciNet: MR4617923
zbMATH: 07731157
Digital Object Identifier: 10.1216/rmj.2023.53.951

Subjects:
Primary: 47A12
Secondary: 47A30

Keywords: inequality , numerical radius , operator norm

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.53 • No. 3 • June 2023
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