A commutative Banach algebra which factorizes but has no approximate units
It is well known that any Banach algebra having bounded approximate units factorizes. For some time it was not clear if, conversely, factorization implied the existence of bounded approximate units. This was disproved by Paschke [3], but the problem remained open for commutative Banach algebras. We...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
March 1976
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| In: |
Proceedings of the American Mathematical Society
Year: 1976, Volume: 55, Issue: 2, Pages: 345-346 |
| ISSN: | 1088-6826 |
| DOI: | 10.1090/S0002-9939-1976-0397312-3 |
| Online Access: | Verlag, kostenfrei, Volltext: http://dx.doi.org/10.1090/S0002-9939-1976-0397312-3
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| Author Notes: | Michael Leinert |
| Summary: | It is well known that any Banach algebra having bounded approximate units factorizes. For some time it was not clear if, conversely, factorization implied the existence of bounded approximate units. This was disproved by Paschke [3], but the problem remained open for commutative Banach algebras. We give an example of a commutative semisimple Banach algebra which factorizes but has not even unbounded approximate units. |
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| Item Description: | Gesehen am 08.06.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1088-6826 |
| DOI: | 10.1090/S0002-9939-1976-0397312-3 |