A generalization of Gelfand-Mazur theorem
In this paper, we show that if A is a unital semisimple complex Banach algebra with only the trivial idempotents and if σA(x) is countable for each x∈Fr(G(A)), then A≅C, this generalizes the Gelfand-Mazur theorem.
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000481 |
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| _version_ | 1832551505573445632 |
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| author | Sung Guen Kim |
| author_facet | Sung Guen Kim |
| author_sort | Sung Guen Kim |
| collection | DOAJ |
| description | In this paper, we show that if A is a unital semisimple complex Banach algebra with
only the trivial idempotents and if σA(x) is countable for each x∈Fr(G(A)), then A≅C, this
generalizes the Gelfand-Mazur theorem. |
| format | Article |
| id | doaj-art-fec24cbc4ac04c01aedac3695beeab92 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-fec24cbc4ac04c01aedac3695beeab922025-02-03T06:01:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116240140210.1155/S0161171293000481A generalization of Gelfand-Mazur theoremSung Guen Kim0Department of Mathematics, Pohang Institute of Science and Technology, P.O. Box 215, Pohang 790-600, KoreaIn this paper, we show that if A is a unital semisimple complex Banach algebra with only the trivial idempotents and if σA(x) is countable for each x∈Fr(G(A)), then A≅C, this generalizes the Gelfand-Mazur theorem.http://dx.doi.org/10.1155/S0161171293000481 |
| spellingShingle | Sung Guen Kim A generalization of Gelfand-Mazur theorem International Journal of Mathematics and Mathematical Sciences |
| title | A generalization of Gelfand-Mazur theorem |
| title_full | A generalization of Gelfand-Mazur theorem |
| title_fullStr | A generalization of Gelfand-Mazur theorem |
| title_full_unstemmed | A generalization of Gelfand-Mazur theorem |
| title_short | A generalization of Gelfand-Mazur theorem |
| title_sort | generalization of gelfand mazur theorem |
| url | http://dx.doi.org/10.1155/S0161171293000481 |
| work_keys_str_mv | AT sungguenkim ageneralizationofgelfandmazurtheorem AT sungguenkim generalizationofgelfandmazurtheorem |