Operator ultra-amenability

Extending M. Daws’ definition of ultra-amenable Banach algebras, we introduce the notion of operator ultra-amenability for completely contractive Banach algebras. For a locally compact group G , we show that the operator ultra-amenability of A ( G ) imposes severe restrictions on G . In particular,...

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Bibliographic Details
Published in:Archiv der Mathematik 2017-05, Vol.108 (5), p.465-471
Main Authors: Forrest, Brian E., Runde, Volker, Schlitt, Kyle
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Subgroups
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Summary:Extending M. Daws’ definition of ultra-amenable Banach algebras, we introduce the notion of operator ultra-amenability for completely contractive Banach algebras. For a locally compact group G , we show that the operator ultra-amenability of A ( G ) imposes severe restrictions on G . In particular, it forces G to be a discrete, amenable group with no infinite abelian subgroups. For various classes of such groups, this means that G is finite.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-016-1012-1