Means on \(CV_ p(G)\)-subspaces of \(CV_ p(G)\) with RNP and Schur property
type: Item
instance of: scholarly article
title: Means on \(CV_ p(G)\)-subspaces of \(CV_ p(G)\) with RNP and Schur property
zbMATH Open document ID: 0675.43001
author: Françoise Lust-Piquard
publication date: 1989-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74864
review text: Let G be a locally compact abelian group and \(CV_ p(G)\) (1\(\leq p\leq 2)\) be the space of bounded convolution operators: \(L^ p(G)\to L^ p(G)\). We generalize to \(CV_ p(G)\) some results which are well known for \(CV_ 2(G)\) (or rather for \(L^{\infty}(\hat G)):\) we define and study ``invariant means'' on \(CV_ p(G)\), and we show that if \(E\subset G\) is compact and scattered the space \(CV_ p(E)\) (convolution operators which are supported on E) has the Schur property and is the norm closure of finitely supported measures. We also give some consequences of these results.
Mathematics Subject Classification ID: 43A07
Mathematics Subject Classification ID: 43A22
Mathematics Subject Classification ID: 46B22
Mathematics Subject Classification ID: 43A46
zbMATH DE Number: 4105568
zbMATH Keywords: Radon-Nikodym property
zbMATH Keywords: locally compact abelian group
zbMATH Keywords: space of bounded convolution operators
zbMATH Keywords: invariant means
zbMATH Keywords: Schur property
zbMATH Keywords: finitely supported measures
MaRDI profile type: Publication
OpenAlex ID: W2319696829
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DOI: 10.5802/AIF.1197
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 4105568