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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 643568, 12 pages
Research Article

Norm for Sums of Two Basic Elementary Operators

A. Bachir,1,2,3 F. Lombarkia,1,2,3 and A. Segres1,2,3

1Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia
2Department of Mathematics, Faculty of Science, University of Batna, 05000 Batna, Algeria
3Department of Mathematics, Mascara University, Algeria

Received 27 July 2012; Revised 8 November 2012; Accepted 25 November 2012

Academic Editor: Yuri Latushkin

Copyright © 2012 A. Bachir et al. 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.


We give necessary and sufficient conditions under which the norm of basic elementary operators attains its optimal value in terms of the numerical range.