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Proceedings of the London Mathematical Society Advance Access published online on October 3, 2009
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdp038
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© 2009 London Mathematical Society

Closed ideal structure and cohomological properties of certain radical Banach algebras

F. Ghahramani

Department of Mathematics
University of Manitoba
Winnipeg, MB
Canada R3T 2N2

C. J. Read

School of Mathematics
University of Leeds
Leeds
LS2 9JT
England
read@maths.leeds.ac.uk

G. A. Willis

School of Mathematical and Physical Sciences
The University of Newcastle
V131, Callaghan
Australia
George.Willis@newcastle.edu.au

Received 30 October 2008. Revision received 27 May 2009.

We further the study of a class of singly generated radical Banach algebras (sometimes called LRRW (Loy, Read, Runde and Willis) algebras after the four authors involved in the original paper) that have compact multiplication and are weakly amenable. First, we characterize the closed ideal structure of these algebras. The closed ideals of an LRRW algebra are identified, and the lattice of closed ideals is shown to be isomorphic to the unit interval. Then we show that LRRW algebras are not approximately amenable and have global homological dimension greater than 1. Furthermore, epimorphisms onto these algebras and derivations from them are continuous.

Research supported by NSERC grant 36640-2007.

2000 Mathematics Subject Classification 46J45, 46M18 (primary), 46H40, 46J20 (secondary).


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