On some properties of elements in hypergroup algebras

Author(s):

Ali Ghaffari

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

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

Keywords:

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

Language:
English
Published:
International Journal Of Nonlinear Analysis And Applications, Volume:13 Issue: 2, Summer-Autumn 2022
Pages:
3307 to 3312
https://magiran.com/p2563412