The Bochner-Schoenberg-Eberlein property for vector-valued Lipschitz algebras

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:479

Article

Abtahi, Fatemeh¹  Kamali, Zeinab^2,3  Toutounchi, Maryam¹ 

[1] Univ Isfahan, Dept Math, Esfahan, Iran

[2] Islamic Azad Univ, Isfahan Khorasgan Branch, Dept Math, Esfahan, Iran

[3] Inst Res Fundamental Sci IPM, Sch Math, Niavarari Bldg,Niavaran Sq, Tehran, Iran

关键词: BSE-algebra;    Lipschitz algebra;    Metric space;   

DOI  :  10.1016/j.jmaa.2019.06.073

来源: Elsevier

【 摘 要 】

Let (K, d) be a compact metric space, 0 < alpha <= 1 and Lip(alpha)K lf the space of the Lipschitz functions on K. It is known that the Banach algebra Lip(alpha)K is a BSE-algebra. In this paper, for a commutative unital semisimple Banach algebra A, we prove that the Banach algebra Lip(alpha)(K, A) of the A-valued Lipschitz functions is a BSE-algebra if and only if A is so. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free