Translator Disclaimer
August 2016 A note concerning the numerical range of a basic elementary operator
Mohamed Boumazgour, Hossam A. Nabwey
Ann. Funct. Anal. 7(3): 434-441 (August 2016). DOI: 10.1215/20088752-3605510

Abstract

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.

Citation

Download Citation

Mohamed Boumazgour. Hossam A. Nabwey. "A note concerning the numerical range of a basic elementary operator." Ann. Funct. Anal. 7 (3) 434 - 441, August 2016. https://doi.org/10.1215/20088752-3605510

Information

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

zbMATH: 1351.47003
MathSciNet: MR3513127
Digital Object Identifier: 10.1215/20088752-3605510

Subjects:
Primary: 47A12
Secondary: 47A30, 47B47

Rights: Copyright © 2016 Tusi Mathematical Research Group

JOURNAL ARTICLE
8 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.7 • No. 3 • August 2016
Back to Top