Annals of Functional Analysis

A note concerning the numerical range of a basic elementary operator

Mohamed Boumazgour and Hossam A. Nabwey

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Let B(H) be the algebra of all bounded linear operators on a complex Hilbert space H, and let S be a norm ideal in B(H). For A,BB(H), define the elementary operator MS,A,B on S by MS,A,B(X)=AXB (XS). The aim of this paper is to give necessary and sufficient conditions under which the equality V(MS,A,B)=co¯(W(A)W(B)) holds. Here V(T) and W(T) denote the algebraic numerical range and spatial numerical range of an operator T, respectively, and co¯(Ω) denotes the closed convex hull of a subset ΩC.

Article information

Ann. Funct. Anal., Volume 7, Number 3 (2016), 434-441.

Received: 6 November 2015
Accepted: 14 January 2016
First available in Project Euclid: 17 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A12: Numerical range, numerical radius
Secondary: 47A30: Norms (inequalities, more than one norm, etc.) 47B47: Commutators, derivations, elementary operators, etc.

numerical range spectrum elementary operators norm ideals


Boumazgour, Mohamed; Nabwey, Hossam A. A note concerning the numerical range of a basic elementary operator. Ann. Funct. Anal. 7 (2016), no. 3, 434--441. doi:10.1215/20088752-3605510.

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