Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 7, Number 3 (2016), 434-441.
A note concerning the numerical range of a basic elementary operator
Let be the algebra of all bounded linear operators on a complex Hilbert space , and let be a norm ideal in . For , define the elementary operator on by (). The aim of this paper is to give necessary and sufficient conditions under which the equality holds. Here and denote the algebraic numerical range and spatial numerical range of an operator , respectively, and denotes the closed convex hull of a subset .
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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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. https://projecteuclid.org/euclid.afa/1466172137