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

Françoise Lust-Piquard

Annales de l'institut Fourier (1989)

  • Volume: 39, Issue: 4, page 969-1006
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Lust-Piquard, Françoise. "Means on $CV_p(G)$-subspaces of $CV_p(G)$ with RNP and Schur property." Annales de l'institut Fourier 39.4 (1989): 969-1006. <http://eudml.org/doc/74864>.

@article{Lust1989,
abstract = {Let $G$ be a locally compact abelian group and $CV_ p(G)$$(1\le p\le 2)$ be the space of bounded convolution operators: $L^ p(G)\rightarrow L^ p(G)$. 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.},
author = {Lust-Piquard, Françoise},
journal = {Annales de l'institut Fourier},
keywords = {Radon-Nikodym property; locally compact abelian group; space of bounded convolution operators; invariant means; Schur property; finitely supported measures},
language = {eng},
number = {4},
pages = {969-1006},
publisher = {Association des Annales de l'Institut Fourier},
title = {Means on $CV_p(G)$-subspaces of $CV_p(G)$ with RNP and Schur property},
url = {http://eudml.org/doc/74864},
volume = {39},
year = {1989},
}

TY - JOUR
AU - Lust-Piquard, Françoise
TI - Means on $CV_p(G)$-subspaces of $CV_p(G)$ with RNP and Schur property
JO - Annales de l'institut Fourier
PY - 1989
PB - Association des Annales de l'Institut Fourier
VL - 39
IS - 4
SP - 969
EP - 1006
AB - Let $G$ be a locally compact abelian group and $CV_ p(G)$$(1\le p\le 2)$ be the space of bounded convolution operators: $L^ p(G)\rightarrow L^ p(G)$. 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.
LA - eng
KW - Radon-Nikodym property; locally compact abelian group; space of bounded convolution operators; invariant means; Schur property; finitely supported measures
UR - http://eudml.org/doc/74864
ER -

References

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