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Hypergroup algebras as topological algebras

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Maghsoudi, S. and Seoane-Sepúlveda, Juan B. (2014) Hypergroup algebras as topological algebras. Bulletin of the Australian Mathematical Society, 90 (3). pp. 486-493. ISSN 0004-9727

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Official URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9391117&fileId=S0004972714000367



Abstract

Let K be a locally compact hypergroup endowed with a left Haar measure and let L1(K) be the usual Lebesgue space of K with respect to the left Haar measure. We investigate some properties of L1(K) under a locally convex topology β1. Among other things, the semireflexivity of (L1(K),β1) and of sequentiallyβ1-continuous functionals is studied. We also show that (L1(K),β1) with the convolution multiplication is always a complete semitopological algebra, whereas it is a topological algebra if and only if K is compact.


Item Type:Article
Uncontrolled Keywords:locally compact hypergroup; strict topology; hypergroup algebra; topological algebra
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:29163
Deposited On:11 Mar 2015 08:58
Last Modified:25 Nov 2016 12:39

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