Abstract
This paper presents an operator theory approach for the abstract structure of Banach function modules over coset spaces of compact subgroups. Let G be a locally compact group and H be a compact subgroup of G. Let \(\mu \) be the normalized G-invariant measure over the homogeneous space G / H associated to the Weil’s formula and \(1\le p<\infty \). We then introduce the notion of convolution left-module action of \(L^1(G/H,\mu )\) on the Banach function spaces \(L^p(G/H,\mu )\).
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Ghaani Farashahi, A. Abstract Banach Convolution Function Modules over Coset Spaces of Compact Subgroups in Locally compact Groups. Bull Braz Math Soc, New Series 53, 357–377 (2022). https://doi.org/10.1007/s00574-018-00129-6
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DOI: https://doi.org/10.1007/s00574-018-00129-6