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

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).