Weighted semigroup measure algebra as a WAP-algebra

2015/01/26 by H. R. Ebrahimi Vishki, Vishki, H. R. Ebrahimi, B. Khodsiani +3 · 1 citation
Mathematics · #43A10 #43A20 #46H15 #46H25 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:43A10 #msc:43A20 #msc:46H15 #msc:46H25

paper · pdf · doi:10.48550/arxiv.1501.06428

arxiv created 2015/01/26 · arxiv updated 2015/01/27

Abstract

Banach algebra A for which the natural embedding x into x^ of A into WAP(A)* is bounded below; that is, for some m in R with m > 0 we have ||x^|| > m ||x||, is called a WAP-algebra. Through we mainly concern with weighted measure algebra M_b(S;w); where w is a weight on a semi-topological semigroup S. We study those con- ditions under which M_b(S;w) is a WAP-algebra (respectively dual Banach algebra). In particular, M_b(S) is a WAP-algebra (respectively dual Banach algebra) if and only if wap(S) separates the points of S (respectively S is compactly cancellative semigroup). We apply our results for improving some older results in the case where S is discrete.

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