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

Section

Articles