Illinois Journal of Mathematics

Abstract convolution function algebras over homogeneous spaces of compact groups

Arash Ghaani Farashahi

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This paper presents a systematic study for structure of abstract Banach function $*$-algebras over homogeneous spaces of compact groups. Let $G$ be a compact group and $H$ be a closed subgroup of $G$. Let $\mu$ be the normalized $G$-invariant measure over the homogeneous space $G/H$ associated to the Weil’s formula and $1\leq p<\infty$. Then we introduce the notions of convolution and involution for the Banach function spaces $L^{p}(G/H,\mu)$.

Article information

Illinois J. Math., Volume 59, Number 4 (2015), 1025-1042.

Received: 9 April 2016
Revised: 7 July 2016
First available in Project Euclid: 27 February 2017

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Primary: 22C05: Compact groups 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 43A20: $L^1$-algebras on groups, semigroups, etc. 43A77: Analysis on general compact groups 43A85: Analysis on homogeneous spaces 47A67: Representation theory


Ghaani Farashahi, Arash. Abstract convolution function algebras over homogeneous spaces of compact groups. Illinois J. Math. 59 (2015), no. 4, 1025--1042. doi:10.1215/ijm/1488186019.

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