Document Type : Research Paper

Author

• Ali Ghaffari

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

Abstract

Let $H$ be a hypergroup with left Haar measure and let $L^1(H)$ be the complex Lebesgue space associated with it. Let $L^{\mathrm{\infty }}(H)$ 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 $\mu F\in L^{\mathrm{\infty }}(H{)}^{\ast }$ 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 $F\in L^{\mathrm{\infty }}(H{)}^{\ast }$, then $F\in L^1(H)$.

Keywords

• Banach algebras
• Discrete topology
• Hypergroup algebras
• Second dual of hypergroup algebras
• Weak topology