Table of Contents
ISRN Mathematical Analysis
Volume 2014, Article ID 246301, 4 pages
http://dx.doi.org/10.1155/2014/246301
Research Article

A Formula for the Numerical Range of Elementary Operators

Department of Mathematics, Faculty of Sciences Semlalia, Marrakech, Morocco

Received 10 November 2013; Accepted 9 February 2014; Published 20 March 2014

Academic Editors: M. Lindstrom and C. Zhu

Copyright © 2014 M. Barraa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be the algebra of bounded linear operators on a complex Hilbert space . For -tuples of elements of and , let denote the elementary operator on defined by . In this paper, we prove the following formula for the numerical range of : , where is the set of unitary operators.