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

The BSE property for vector-valued Frechet Lipschitz algebras

“…That the Lipschitz algebra Lip α (K, A) is a BSE-algebra if and only if A is a BSEalgebra, where K is a compact metric space, A is a commutative unital semisimple Banach algebra, and 0 < α ≤ 1 is proved in [1]. In this article, this result is generalized, for any metric space (X, d) and any commutative semisimple Frechet algebra (A, p l ).…”

The Bochner–schoenberg-Eberlein Property of Extensions of Banach Algebras and Banach Modules

“…In the next section, we characterise multipliers on A ⊕ 1 X and answer question (1). We show that A ⊕ 1 X is a BSE Banach algebra if and only if A is a BSE Banach algebra and X = {0}.…”

“…This notion was introduced by Takahasi and Hatori in [16] and it is characterised by Kaniuth and Ülger in [11]. Classes of Banach algebras that are BSE Banach algebras and are not BSE Banach algebras have been investigated in [1,5,7,8,9,10]. Takahasi, in [15], generalised the BSE-property to Banach modules.…”

$C_{BSE}(Δ(A))$ as a dual Banach algebra

“…In the case where A is the field of complex numbers C, to simplify the notation, we will write Lip d X and lip d X, rather than Lip d (K, C) and lip d (X, C), respectively. Recently, some important algebraic properties of Lipschitz algebras have been investigated; see [1], [2] and [3]. Here, we study another feacure of this algebras.…”