A note on M -ideals in certain algebras of operators

Chong-Man Cho and Woo Suk Roh

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 23, 1-5

Abstract:

Let X = ( ∑ n = 1 ∞ ℓ 1 n ) 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 ) .

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:907506

DOI: 10.1155/S0161171200002246

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