Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/933383
- Title
- Amenable and weakly amenable Banach algebras with compact multiplication
- Author/Creator
-
Loy, R. J.;
Read, C. J.;
Runde, V.;
Willis, G. A.
- Description
- We investigate amenable and weakly amenable Banach algebras with compact multiplication. Any amenable Banach algebra with compact multiplication is biprojective. As a consequence, every semisimple such algebra which has the approximation property is a topological direct sum of full matrix algebras. In the radical case no such structure theorem is at hand. We also investigate Banach algebras which have a bounded approximate identity consisting of normalized powers of an element x. Any such Banach algebra is either unital or radical; if the algebra is also generated by x, it is weakly amenable. We construct a radical example with compact multiplication which moreover is an integral domain. This furnishes a new example of a commutative, weakly amenable, non-amenable, radical Banach algebra.
- Relation
- Journal of Functional Analysis Vol. 17, Issue 1, p. 78-114
- Publisher Link
- http://dx.doi.org/10.1006/jfan.1999.3533
- Date
- 2000
- Publisher
- Elsevier
- Keyword(s)
-
Banach algebras;
compact multiplication;
group algebra;
functional mathematics
- Resource Type
- journal article
- Identifier
- http://hdl.handle.net/1959.13/933383
- Identifier
- ISSN:0022-1236
- Language
- eng
- Reviewed
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