Remarks on Segal algebras
Let B be an abstract Segal algebra in some Banach algebra A. There was some belief that in the commutative case A should be semi-simple, if B is, but this is not so (Section I). It is well known that a (proper) abstract Segal algebra does not have bounded right approximate units. It may however have...
Gespeichert in:
| 1. Verfasser: | |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
1975
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| In: |
Manuscripta mathematica
Year: 1975, Jahrgang: 16, Heft: 1, Pages: 1-9 |
| ISSN: | 1432-1785 |
| DOI: | 10.1007/BF01169059 |
| Online-Zugang: | Verlag, Volltext: http://dx.doi.org/10.1007/BF01169059 Verlag, Volltext: https://link.springer.com/article/10.1007/BF01169059 
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| Verfasserangaben: | Michael Leinert |
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| 520 | |a Let B be an abstract Segal algebra in some Banach algebra A. There was some belief that in the commutative case A should be semi-simple, if B is, but this is not so (Section I). It is well known that a (proper) abstract Segal algebra does not have bounded right approximate units. It may however have a left unit. Pseudosymmetric Segal algebras in the sense of Reiter do not have bounded left approximate units (Section II). A nonfactorization proof is given for a class of algebras which contains most of the known examples of Segal algebras on abelian groups (Section III). | ||
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