BSE-Property for Some Certain Segal and Banach Algebras View Full Text


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Article Info

DATE

2019-04

AUTHORS

Mohammad Fozouni, Mehdi Nemati

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. In addition, in the case that G is discrete, we show that Acb(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. More... »

PAGES

38

References to SciGraph publications

  • 2009. A Course in Commutative Banach Algebras in NONE
  • 2014-04. The Bochner-Schoenberg-Eberlein Property for in JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00009-019-1305-2

    DOI

    http://dx.doi.org/10.1007/s00009-019-1305-2

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