On some properties of elements in hypergroup algebras

Document Type : Research Paper


Department of Mathematics, University of Semnan, P. O. Box 35195-363, Semnan, Iran


Let $H$ be a hypergroup with left Haar measure and let $L^1(H)$ be the complex Lebesgue space associated with it. Let $L^\infty(H)$ be the set of all locally measurable functions that are bounded except on a locally null set, modulo functions that are zero locally a.e. Let $\mu\in M(H)$. We want to find out when $\mu F\in L^\infty(H)^*$ implies that $F\in L^1(H)$. Some necessary and sufficient conditions is found for a measure $\mu$ for which if $\mu F\in L^1(H)$ for every $F\in L^\infty(H)^*$, then $F\in L^1(H)$.


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Volume 13, Issue 2
July 2022
Pages 3307-3312
  • Receive Date: 04 April 2021
  • Revise Date: 17 June 2021
  • Accept Date: 19 October 2021