On the inequality w(AB) ≤ c||A||w(B) where A is a positive operator-Reference-Cited by-同舟云学术

On the inequality w(AB) ≤ c||A||w(B) where A is a positive operator

Published:2022 Issue:4 Volume:36 Page:1337-1340
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Benabdi El¹,Baghdad Abderrahim²,Kaadoud Mohamed²,Barraa Mohamed²

Affiliation:

1. Department of Mathematics, Laboratory of Mathematics, Statistics and Applications, Faculty of Sciences, Mohammed V University in Rabat, Rabat, Morocco

2. Department of Mathematics, Faculty of Sciences-Semlalia, University Cadi Ayyad, Marrakesh, Morocco

Abstract

Abu-Omar and Kittaneh [Numerical radius inequalities for products of Hilbert space operators, J. Operator Theory 72(2) (2014), 521-527], wonder what is the smallest constant c such thatw(AB) ? c||A||w(B) for all bounded linear operators A, B on a complex Hilbert space with A is positive. Here, w(?) stands for the numerical radius. In this paper, we prove that c = 3?3/4.

Publisher

National Library of Serbia

Subject

General Mathematics

Reference6 articles.

1. A. Abu-Omar, F. Kittaneh, Numerical radius inequalities for products of Hilbert space operators, J. Operator Theory 72(2) (2014) 521-527.

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3. K. E. Gustafson, D. K. M. Rao, Numerical range: The Field of Values of Linear Operators and Matrices, Springer, New York, NY, USA, 1997.

4. V. Müller, The numerical radius of a commuting product, Michigan Math. J. 35 (1988) 255-260.

5. K. Okubo, T. Ando, Operator radii of commuting products, Proc. Amer. Math. Soc. 56 (1976) 203-210.

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