## “School of Mathematics”

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Paper   IPM / M / 16715
 School of Mathematics Title: Weakly compact multipliers and \Varphi-amenable Banach algebras Author(s): Mehdi Nemati (Joint with Zh. Sohaei) Status: To Appear Journal: Rocky Mountain J. Math. Supported by: IPM
Abstract:
et A be a Banach algebra and let J be a closed ideal of A such that φ|J ≠ 0 for some non-zero character φ on A. In this paper, we obtain some relations between the existence of compact and weakly compact multipliers on J and on A in some sense. Then we apply these results to hypergroup algebra L1(K) when K is a locally compact hypergroup. In particular, for a closed ideal J in L1(K) we prove that K is compact if and only if there is fJ such that φ1(f) ≠ 0 and the multiplication operator λf:gg*f is weakly compact on J. Using this, we study Arens regularity of J whenever it has a bounded left approximate identity. Finally, we apply these results on some abstract Segal algebras with respect to the L1(K).