BSE-property for some certain Segal and Banach algebras

2016/04/06 by Mohammad Fozouni, Fozouni, Mohammad, Mehdi Nemati +1
Mathematics · #22D05 #43A25 #46H05 #46J10 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:22D05 #msc:43A25 #msc:46H05 #msc:46J10

paper · pdf · doi:10.48550/arxiv.1604.01496

13 pages

arxiv created 2018/12/18 · arxiv updated 2018/12/19

Abstract

For a commutative semi-simple Banach algebra A which is an ideal in its second dual we give a necessary and sufficient condition for an essential abstract Segal algebra in A to be a BSE-algebra. We show that a large class of abstract Segal algebras in the Fourier algebra A(G) of a locally compact group G are BSE-algebra if and only if they have bounded weak approximate identities. Also, in the case that G is discrete we show that A_{\rm cb}(G) is a BSE-algebra if and only if G is weakly amenable. We study the BSE-property of some certain Segal algebras implemented by local functions that were recently introduced by J. Inoue and S.-E. Takahasi. Finally we give a similar construction for the group algebra implemented by a measurable and sub-multiplicative function.

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