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International Journal of Mathematics and Mathematical Sciences
Volume 23, Issue 10, Pages 681-685

A note on M-ideals in certain algebras of operators

Department of Mathematics, Hanyang University, Seoul 133-791, Korea

Received 7 October 1998

Copyright © 2000 Hindawi Publishing Corporation. 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.


Let X=(n=11n)p,p>1. In this paper, we investigate M-ideals which are also ideals in L(X), the algebra of all bounded linear operators on X. We show that K(X), the ideal of compact operators on X is the only proper closed ideal in L(X) which is both an ideal and an M-ideal in L(X).