Background
Type: Article

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

Journal: Journal of Mathematical Analysis and Applications (0022247X)Year: 2019/11/01Volume: Issue: 1
Abtahi F.aKamali Z. Toutounchi M.
DOI:10.1016/j.jmaa.2019.06.073Language: English

Abstract

Let (K,d) be a compact metric space, 0<α≤1 and LipαK the space of the Lipschitz functions on K. It is known that the Banach algebra LipαK is a BSE-algebra. In this paper, for a commutative unital semisimple Banach algebra A, we prove that the Banach algebra Lipα(K,A) of the A-valued Lipschitz functions is a BSE-algebra if and only if A is so. © 2019 Elsevier Inc.