Means on \(CV_ p(G)\)-subspaces of \(CV_ p(G)\) with RNP and Schur property
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.
scientific article; zbMATH DE number 4105568
scientific article