Let S be an inverse semigroup with an upward directed set of idempotents E. In this paper we define the module topological center of second dual of a Banach algebra which is a Banach module over another Banach algebra with compatible actions, and find it for ℓ 1 (S) * * (as an ℓ 1 (E)-module). We also prove that ℓ 1 (S) * * is ℓ 1 (E)-module amenable if and only if an appropriate group homomorphic image of S is finite.2000 Mathematics Subject Classification. 46H25.
In this paper, we introduce new concept of orthogonal cone metric spaces. We stablish new versions of fixed point theorems in incomplete orthogonal cone metric spaces. As an application, we show the existence and uniqueness of solution of the periodic boundry value problem.
The last equivalence of the display in the proof of Theorem 2.2 (page 301) is not correct (and b ∈ A is missing inside the brackets of the fourth line of this display). As noted at the beginning of this section, A has a natural O-module structure defined by α.λ(a) = λ(a.α), λ.α(a) = λ(α.a) (α ∈ O, a ∈ A, λ ∈ A). We need to modify Definition 2.1 as follows. Definition 2.1 A is called module Arens regular (as an O-module) if the operator R λ : A → A ; a → a.λ is weakly compact for any λ ∈ A satisfying λ(α.ab) = Communicated by Jerome A. Goldstein.
In this article, following Gorgi and Yazdanpanah, we define two new concepts of the ideal amenability for a Banach algebra A. We compare these notions with J-weak amenability and ideal amenability, where J is a closed two-sided ideal in A. We also study the hereditary properties of quotient ideal amenability for Banach algebras. Some examples show that the concepts of A/J-weak amenability and of J-weak amenability do not coincide for Banach algebras in general.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.