Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 7, Number 4 (2016), 564-572.
Character amenability and contractibility of some Banach algebras on left coset spaces
Let be a compact subgroup of a locally compact group , and let be a strongly quasi-invariant Radon measure on the homogeneous space . In this article, we show that every element of , the character space of , determines a nonzero multiplicative linear functional on . Using this, we prove that for all , the right -amenability of and the right -amenability of are both equivalent to the amenability of . Also, we show that , as well as , is right -contractible if and only if is compact. In particular, when is the trivial subgroup, we obtain the known results on group algebras and measure algebras.
Ann. Funct. Anal., Volume 7, Number 4 (2016), 564-572.
Received: 16 December 2015
Accepted: 20 March 2016
First available in Project Euclid: 31 August 2016
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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