International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 10, Pages 681-685
doi:10.1155/S0161171200002246
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 Chong-Man Cho and Woo Suk Roh. 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 X=(∑n=1∞ℓ1n)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).