The compactum and finite dimensionality in Banach algebras
Given a Banach algebra A, the compactum of A is defined to be the set of elements x∈A such that the operator a→xax is compact. General properties of the compactum and its relation to the socle of A are discussed. Characterizations of finite dimensionality of a semi-simple Banach algebra are given in...
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| Format: | Article |
| Language: | English |
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Wiley
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171282000246 |
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| _version_ | 1832545826528821248 |
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| author | Abdullah H. Al-Moajil |
| author_facet | Abdullah H. Al-Moajil |
| author_sort | Abdullah H. Al-Moajil |
| collection | DOAJ |
| description | Given a Banach algebra A, the compactum of A is defined to be the set of elements x∈A such that the operator a→xax is compact. General properties of the compactum and its relation to the socle of A are discussed. Characterizations of finite dimensionality of a semi-simple Banach algebra are given in terms of the compactum and the socle of A. |
| format | Article |
| id | doaj-art-f9d2403f559f4015a0be92b01c4d7d1a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1982-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f9d2403f559f4015a0be92b01c4d7d1a2025-02-03T07:24:45ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251982-01-015227528010.1155/S0161171282000246The compactum and finite dimensionality in Banach algebrasAbdullah H. Al-Moajil0Gulf Organization for Industrial Consulting, P.O. Box 5114, Doha, QatarGiven a Banach algebra A, the compactum of A is defined to be the set of elements x∈A such that the operator a→xax is compact. General properties of the compactum and its relation to the socle of A are discussed. Characterizations of finite dimensionality of a semi-simple Banach algebra are given in terms of the compactum and the socle of A.http://dx.doi.org/10.1155/S0161171282000246compact operatorssocleminimal idempotentspectrum. |
| spellingShingle | Abdullah H. Al-Moajil The compactum and finite dimensionality in Banach algebras International Journal of Mathematics and Mathematical Sciences compact operators socle minimal idempotent spectrum. |
| title | The compactum and finite dimensionality in Banach algebras |
| title_full | The compactum and finite dimensionality in Banach algebras |
| title_fullStr | The compactum and finite dimensionality in Banach algebras |
| title_full_unstemmed | The compactum and finite dimensionality in Banach algebras |
| title_short | The compactum and finite dimensionality in Banach algebras |
| title_sort | compactum and finite dimensionality in banach algebras |
| topic | compact operators socle minimal idempotent spectrum. |
| url | http://dx.doi.org/10.1155/S0161171282000246 |
| work_keys_str_mv | AT abdullahhalmoajil thecompactumandfinitedimensionalityinbanachalgebras AT abdullahhalmoajil compactumandfinitedimensionalityinbanachalgebras |