Characterizations of Riesz sets

Authors

  • A. Ülger

DOI:

https://doi.org/10.7146/math.scand.a-15171

Abstract

Let G be a compact abelian group, M(G) its measure algebra and L1(G) its group algebra. For a subset E of the dual group ˆG, let ME(G)={μM(G):ˆμ=0 on ˆGE} and L1E(G)={aL1(G):ˆa=0 on ˆGE}. The set E is said to be a Riesz set if ME(G)=L1E(G). In this paper we present several characterizations of the Riesz sets in terms of Arens multiplication and in terms of the properties of the Gelfand transform Γ:L1E(G)c0(E).

Downloads

Published

2011-06-01

How to Cite

Ülger, A. (2011). Characterizations of Riesz sets. MATHEMATICA SCANDINAVICA, 108(2), 264–278. https://doi.org/10.7146/math.scand.a-15171

Issue

Section

Articles