The Bochner–Schoenberg–Eberlein Property for Total

Authors: Zeinab Kamali Mahmood Lashkarizadeh Bami

Publish Date: 2015/12/17

Volume: 22, Issue: 6, Pages: 1225-1234

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Abstract

The concepts of BSE property and BSE algebras were introduced and studied by Takahasi and Hatori in 1990 and later by Kaniuth and Ülger This abbreviation refers to a famous theorem proved by Bochner and Schoenberg for L1mathbb R where mathbb R is the additive group of real numbers and by Eberlein for L1G of a locally compact abelian group G In this paper we investigate this property for the Banach algebra LpSmu 1le pinfty where S is a compact totally ordered semigroup with multiplication xy=max xy and mu is a regular bounded continuous measure on S As an application we have shown that L1Smu is not an ideal in its second dualThe authors would like to thank the referees of the paper for the invaluable comments and suggestions which serve to improve the paper The first author’s research was supported in part by a grant from IAU Isfahan branch and IPM No 93470066 The second author acknowledge that this research was supported by the Center of Excellence for Mathematics and the office of Graduate Studies of the University of Isfahan

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