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 |
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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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| _version_ | 1832567514797703168 |
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| author | Chong-Man Cho Woo Suk Roh |
| author_facet | Chong-Man Cho Woo Suk Roh |
| author_sort | Chong-Man Cho |
| collection | DOAJ |
| description | 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). |
| format | Article |
| id | doaj-art-50b15ee52b334177895c2ef9a88b46b2 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-50b15ee52b334177895c2ef9a88b46b22025-02-03T01:01:13ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-01231068168510.1155/S0161171200002246A note on M-ideals in certain algebras of operatorsChong-Man Cho0Woo Suk Roh1Department of Mathematics, Hanyang University, Seoul 133-791, KoreaDepartment of Mathematics, Hanyang University, Seoul 133-791, KoreaLet 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).http://dx.doi.org/10.1155/S0161171200002246Compact operatorsidealM-ideal.. |
| spellingShingle | Chong-Man Cho Woo Suk Roh A note on M-ideals in certain algebras of operators International Journal of Mathematics and Mathematical Sciences Compact operators ideal M-ideal.. |
| title | A note on M-ideals in certain algebras of
operators |
| title_full | A note on M-ideals in certain algebras of
operators |
| title_fullStr | A note on M-ideals in certain algebras of
operators |
| title_full_unstemmed | A note on M-ideals in certain algebras of
operators |
| title_short | A note on M-ideals in certain algebras of
operators |
| title_sort | note on m ideals in certain algebras of operators |
| topic | Compact operators ideal M-ideal.. |
| url | http://dx.doi.org/10.1155/S0161171200002246 |
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