%0 Journal Article
%T On some properties of elements in hypergroup algebras
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Ghaffari, Ali
%D 2022
%\ 07/01/2022
%V 13
%N 2
%P 3307-3312
%! On some properties of elements in hypergroup algebras
%K Banach algebras
%K discrete topology
%K Hypergroup algebras
%K Second dual of hypergroup algebras
%K Weak topology
%R 10.22075/ijnaa.2021.23709.3960
%X 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 $F\in L^1(H)$.
%U https://ijnaa.semnan.ac.ir/article_7401_120da88299bb964015cb0bdccb1b9e97.pdf