Weighted semigroup measure algebra as a WAP-algebra
Functional Analysis
2015-01-27 v1
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.
Cite
@article{arxiv.1501.06428,
title = {Weighted semigroup measure algebra as a WAP-algebra},
author = {H. R. Ebrahimi Vishki and B. Khodsiani and A. Rejali},
journal= {arXiv preprint arXiv:1501.06428},
year = {2015}
}