TY - JOUR
ID - 7401
TI - On some properties of elements in hypergroup algebras
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Ghaffari, Ali
AD - Department of Mathematics, University of Semnan, P. O. Box 35195-363, Semnan, Iran
Y1 - 2022
PY - 2022
VL - 13
IS - 2
SP - 3307
EP - 3312
KW - Banach algebras
KW - discrete topology
KW - Hypergroup algebras
KW - Second dual of hypergroup algebras
KW - Weak topology
DO - 10.22075/ijnaa.2021.23709.3960
N2 - 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 $F\in L^1(H)$.
UR - https://ijnaa.semnan.ac.ir/article_7401.html
L1 - https://ijnaa.semnan.ac.ir/article_7401_120da88299bb964015cb0bdccb1b9e97.pdf
ER -