Finite dimensionality in scole of Banach algebras
It is shown that if the socle soc(A) of a semisimple Banach algebra A is norm-closed, then soc(A) is already finite dimensional. The proof makes use of the Al-Moajil theorem. However it is remarked that our main theorem is an extension of the Al-Moajil's.
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171284000570 |
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| _version_ | 1832568214146514944 |
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| author | Sin-Ei Takahasi |
| author_facet | Sin-Ei Takahasi |
| author_sort | Sin-Ei Takahasi |
| collection | DOAJ |
| description | It is shown that if the socle soc(A) of a semisimple Banach algebra A is norm-closed, then soc(A) is already finite dimensional. The proof makes use of the Al-Moajil theorem. However it is remarked that our main theorem is an extension of the Al-Moajil's. |
| format | Article |
| id | doaj-art-56d7d162337c4b5db774500f6d1598da |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-56d7d162337c4b5db774500f6d1598da2025-02-03T00:59:26ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017351952210.1155/S0161171284000570Finite dimensionality in scole of Banach algebrasSin-Ei Takahasi0Department of Mathematics, Ibaraki University, Mito, Ibaraki 310, JapanIt is shown that if the socle soc(A) of a semisimple Banach algebra A is norm-closed, then soc(A) is already finite dimensional. The proof makes use of the Al-Moajil theorem. However it is remarked that our main theorem is an extension of the Al-Moajil's.http://dx.doi.org/10.1155/S0161171284000570compactrumsocleminimal idempotentminimal left idealannihilator. |
| spellingShingle | Sin-Ei Takahasi Finite dimensionality in scole of Banach algebras International Journal of Mathematics and Mathematical Sciences compactrum socle minimal idempotent minimal left ideal annihilator. |
| title | Finite dimensionality in scole of Banach algebras |
| title_full | Finite dimensionality in scole of Banach algebras |
| title_fullStr | Finite dimensionality in scole of Banach algebras |
| title_full_unstemmed | Finite dimensionality in scole of Banach algebras |
| title_short | Finite dimensionality in scole of Banach algebras |
| title_sort | finite dimensionality in scole of banach algebras |
| topic | compactrum socle minimal idempotent minimal left ideal annihilator. |
| url | http://dx.doi.org/10.1155/S0161171284000570 |
| work_keys_str_mv | AT sineitakahasi finitedimensionalityinscoleofbanachalgebras |