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|Paper IPM / M / 16715||
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 f ∈ J such that φ1(f) ≠ 0 and the multiplication operator λf:g→ g*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).
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