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Means on C V p ( G ) -subspaces of C V p ( G ) with RNP and Schur property

Françoise Lust-Piquard — 1989

Annales de l'institut Fourier

Let G be a locally compact abelian group and C V p ( G ) ( 1 p 2 ) be the space of bounded convolution operators: L p ( G ) L p ( G ) . We generalize to C V p ( G ) some results which are well known for C V 2 ( G ) (or rather for L ( G ^ ) ): we define and study “invariant means” on C V p ( G ) , and we show that if E G is compact and scattered the space C V 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.

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