A note on M-ideals in certain algebras of operators
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)....
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200002246 |
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| Summary: | 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). |
|---|---|
| ISSN: | 0161-1712 1687-0425 |