Amenable and weakly amenable Banach algebras with compact multiplication

Title: Amenable and weakly amenable Banach algebras with compact multiplication
Creator: Loy, R. J.; Read, C. J.; Runde, V.; Willis, G. A.
Relation: Journal of Functional Analysis Vol. 17, Issue 1, p. 78-114
Publisher Link: http://dx.doi.org/10.1006/jfan.1999.3533
Publisher: Elsevier
Resource Type: journal article
Date: 2000
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.
Subject: Banach algebras; compact multiplication; group algebra; functional mathematics
Identifier: http://hdl.handle.net/1959.13/933383
Identifier: uon:11618
Identifier: ISSN:0022-1236
Language: eng
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