Annals of Functional Analysis

Character amenability and contractibility of some Banach algebras on left coset spaces

M. Ramezanpour, N. Tavallaei, and B. Olfatian Gillan

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Abstract

Let H be a compact subgroup of a locally compact group G, and let μ be a strongly quasi-invariant Radon measure on the homogeneous space G/H. In this article, we show that every element of G/Hˆ, the character space of G/H, determines a nonzero multiplicative linear functional on L1(G/H,μ). Using this, we prove that for all ϕG/Hˆ, the right ϕ-amenability of L1(G/H,μ) and the right ϕ-amenability of M(G/H) are both equivalent to the amenability of G. Also, we show that L1(G/H,μ), as well as M(G/H), is right ϕ-contractible if and only if G is compact. In particular, when H is the trivial subgroup, we obtain the known results on group algebras and measure algebras.

Article information

Source
Ann. Funct. Anal., Volume 7, Number 4 (2016), 564-572.

Dates
Received: 16 December 2015
Accepted: 20 March 2016
First available in Project Euclid: 31 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.afa/1472659942

Digital Object Identifier
doi:10.1215/20088752-3661431

Mathematical Reviews number (MathSciNet)
MR3543148

Zentralblatt MATH identifier
06621461

Subjects
Primary: 43A20: $L^1$-algebras on groups, semigroups, etc.
Secondary: 46H05: General theory of topological algebras 43A07: Means on groups, semigroups, etc.; amenable groups

Keywords
Banach algebra homogeneous space character amenability

Citation

Ramezanpour, M.; Tavallaei, N.; Olfatian Gillan, B. Character amenability and contractibility of some Banach algebras on left coset spaces. Ann. Funct. Anal. 7 (2016), no. 4, 564--572. doi:10.1215/20088752-3661431. https://projecteuclid.org/euclid.afa/1472659942


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