With this paper, we intend to provide an overview of some recent work on a problem on unbounded derivations of Banach algebras that still defies solution, the non-commutative Singer-Wermer conjecture. In particular, we discuss several global as well as local properties of derivations entailing quasinilpotency in the image.
In this paper we investigate -weak character amenability of certain Banach algebras such as projective tensor product and Lau product , where and are two arbitrary Banach algebras and , the character space of . We also investigate -weak character amenability of abstract Segal algebras and module extension Banach algebras.
In this paper, we generalize the concept of -multipliers on Banach algebras to a class of topological algebras. Then the characterizations of -multipliers are investigated in these algebras.