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

El Benabdi, Abderrahim Baghdad, Mohamed Kaadoud, Mohamed Barraa

Type: Article

Publication Date: 2022-01-01

Citations: 1

DOI: https://doi.org/10.2298/fil2204337b

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.

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Works Cited by This (6)

Action	Title	Year	Authors
+ PDF Chat	The numerical radius of a commuting product.	1988	Veronika Müller
+ PDF Chat	On upper and lower bounds of the numerical radius and an equality condition	2007	Takeaki Yamazaki
+ PDF Chat	Operator radii of commuting products	1976	Kimihiro Okubo T. Andô
+ PDF Chat	Scalar approximants of quadratic operators with applications	2018	Amer Abu-Omar Pei Yuan Wu
+	Numerical radius inequalities for products of Hilbert space operators	2014	Amer Abu-Omar Fuad Kittaneh
+	Numerical Range	1997	Karl E. Gustafson Duggirala K. M. Rao