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2015 Structural transition between $L^{p}(G)$ and $L^{p}(G/H)$
Behrooz Olfatian Gillan, Mohammad Ramezanpour, Narguess Tavallaei
Banach J. Math. Anal. 9(3): 194-205 (2015). DOI: 10.15352/bjma/09-3-14


Let $H$ be a compact subgroup of a locally compact group $G$. We consider the homogeneous space $G/H$ equipped with a strongly quasi-invariant Radon measure $\mu$. For $1\leq p\leq +\infty$, we introduce a norm decreasing linear map from $L^{p}(G)$ onto $L^{p}(G/H,\mu)$ and show that $L^{p}(G/H,\mu)$ may be identified with a quotient space of $L^{p}(G)$. Also, we prove that $L^{p}(G/H,\mu)$ is isometrically isomorphic to a closed subspace of $L^{p}(G)$. These help us study the structure of the classical Banach spaces constructed on a homogeneous space via those created on topological groups.


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Behrooz Olfatian Gillan. Mohammad Ramezanpour. Narguess Tavallaei. "Structural transition between $L^{p}(G)$ and $L^{p}(G/H)$." Banach J. Math. Anal. 9 (3) 194 - 205, 2015.


Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1314.43005
MathSciNet: MR3296134
Digital Object Identifier: 10.15352/bjma/09-3-14

Primary: 43A15
Secondary: 43A85 , 46B25

Keywords: classical Banach space , homogeneous space , Locally compact topological group , strongly quasi--invariant measure

Rights: Copyright © 2015 Tusi Mathematical Research Group

Vol.9 • No. 3 • 2015
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