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On some properties of elements in hypergroup algebras | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، شماره 2، مهر 2022، صفحه 3307-3312 اصل مقاله (331.97 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23709.3960 | ||
| نویسنده | ||
| Ali Ghaffari* | ||
| Department of Mathematics, University of Semnan, P. O. Box 35195-363, Semnan, Iran | ||
| تاریخ دریافت: 15 فروردین 1400، تاریخ بازنگری: 27 خرداد 1400، تاریخ پذیرش: 27 مهر 1400 | ||
| چکیده | ||
| 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 $F\in L^1(H)$. | ||
| کلیدواژهها | ||
| Banach algebras؛ Discrete topology؛ Hypergroup algebras؛ Second dual of hypergroup algebras؛ Weak topology | ||
| مراجع | ||
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