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Translation invariant linear functionals on segal algebras

Published online by Cambridge University Press:  17 April 2009

Yuji Takahashi
Yuji Takahashi
Affiliation:
Department of Mathematics Kushiro Public, University of Economics, 4-1-1 Ashino, Kushiro 085, Japan
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Abstract

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Let S(G) be a Segal algebra on an infinite compact Abelian group G. We study the existence of many discontinuous translation invariant linear functionals on S(G). It is shown that if G/CG contains no finitely generated dense subgroups, then the dimension of the linear space of all translation invariant linear functionals on S(G) is greater than or equal to 2C and there exist 2C discontinuous translation invariant linear functionals on S(G), where c and CG denote the cardinal number of the continuum and the connected component of the identity in G, respectively.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 2 , October 1990 , pp. 287 - 292
Copyright
Copyright © Australian Mathematical Society 1990

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