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ESSENTIAL CHARACTER AMENABILITY OF BANACH ALGEBRAS

Part of: Abstract harmonic analysis Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  01 November 2011

RASOUL NASR-ISFAHANI  and
MEHDI NEMATI
RASOUL NASR-ISFAHANI*
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (email: isfahani@cc.iut.ac.ir)
MEHDI NEMATI
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (email: m.nemati@math.iut.ac.ir)
*
✉For correspondence; e-mail: isfahani@cc.iut.ac.ir
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Abstract

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For a Banach algebra 𝒜 and a character ϕ on 𝒜, we introduce and study the notion of essential ϕ-amenability of 𝒜. We give some examples to show that the class of essentially ϕ-amenable Banach algebras is larger than that of ϕ-amenable Banach algebras introduced by Kaniuth et al. [‘On ϕ-amenability of Banach algebras’, Math. Proc. Cambridge Philos. Soc.144 (2008), 85–96]. Finally, we characterize the essential ϕ-amenability of various Banach algebras related to locally compact groups.

Keywords

Banach algebracharacter amenabilityessential amenabilitylocally compact group

MSC classification

Secondary: 43A07: Means on groups, semigroups, etc.; amenable groups 46H05: General theory of topological algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 3 , December 2011 , pp. 372 - 386
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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