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December 2021 Refinements of norm and numerical radius inequalities
Pintu Bhunia, Kallol Paul
Rocky Mountain J. Math. 51(6): 1953-1965 (December 2021). DOI: 10.1216/rmj.2021.51.1953

Abstract

Several refinements of norm and numerical radius inequalities of bounded linear operators on a complex Hilbert space are given. In particular, we show that if A is a bounded linear operator on a complex Hilbert space, then

14A*A+AA*18A+A*2+AA*2+c2(A+A*)+c2(AA*)w2(A)

and

12AA+AA14(A+A)2(AA)212w2(A)12AA+AA,

where , w() and c() are the operator norm, the numerical radius and the Crawford number, respectively. Further, we prove that if A,D are bounded linear operators on a complex Hilbert space, then

AD01(1t)(A2+D2)/2+tADI2dt1212A2+D2,

where |A|2=AA and |D|2=DD. This is a refinement of a well-known inequality obtained by Bhatia and Kittaneh.

Citation

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Pintu Bhunia. Kallol Paul. "Refinements of norm and numerical radius inequalities." Rocky Mountain J. Math. 51 (6) 1953 - 1965, December 2021. https://doi.org/10.1216/rmj.2021.51.1953

Information

Received: 12 November 2020; Revised: 4 April 2021; Accepted: 6 April 2021; Published: December 2021
First available in Project Euclid: 22 March 2022

Digital Object Identifier: 10.1216/rmj.2021.51.1953

Subjects:
Primary: 47A12
Secondary: 47A30

Keywords: ‎bounded linear operator , Hilbert space , norm inequality , numerical radius , operator convex function

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 6 • December 2021
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