Weakly almost periodic Banach algebras on semi-groups

2015/01/26 by B. Khodsiani, Bahram Khodsiani, Khodsiani, Bahram +2
Mathematics · #43A10 #43A20 #46H15 #46H25 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:43A10 #msc:43A20 #msc:46H15 #msc:46H25

paper · pdf · doi:10.48550/arxiv.1501.06417

arxiv created 2015/01/26 · openalex publication_date 2015/01/26 · arxiv updated 2015/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let WAP(A) be the space of all weakly almost periodic functionals on a Banach algebra A. The Banach algebra A for which the natural embedding of A into WAP(A)* is bounded below is called a WAP-algebra. We show that the second dual of a Banach algebra A is a WAP-algebra, under each Arens products, if and only if A** is a dual Banach algebra. This is equivalent to the Arens regularity of A. For a locally compact foundation semigroup S, we show that the absolutely continuous semigroup measure algebra M_a(S) is a WAP-algebra if and only if the measure algebra M_b(S) is so.

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