Hypergroup algebras as topological algebras

S. Maghsoudi; J. B. Seoane-Sepulveda

Hypergroup algebras as topological algebras

Authors

S. Maghsoudi
J. B. Seoane-Sepulveda Universidad Complutense de Madrid

Keywords:

locally compact hypergroup, strict topology, hypergroup algebra, topological algebra.

Abstract

Let

$K$ be a locally compact hypergroup endowed with a left Haar measure and let

$L^1(K)$ be the usual Lebesgue space of

$K$ with respect to the left Haar measure. We investigate some properties of

$L^1(K)$ under a locally convex topology

$\beta^1$ . Among other things, the semireflexivity of

$(L^1(K), \beta^1)$ and of sequentially

$\beta^1$ -continuous functionals are studied. We also show that

$(L^1(K), \beta^1)$ with the convolution multiplication is always a complete semi-topological algebra whereas it is a topological algebra if and only if

$K$ is compact. DOI:- 10.1017/S0004972714000367

Published

2014-09-20

Issue

Vol. 90 No. 3 (2014)

Section

Articles

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