Let  be a Banach algebra and let ** be the second dual algebra of  endowed with the first or the second Arens product. We investigate relations between amenability of ** and Arens regularity of  and the rôle topological centres in amenability of **. We also find conditions under which weak amenability of ** implies weak amenability of .

No abstract

No abstract

In this paper, we investigate the notion φ-injectivity for Banach A-modules, where φ is a character on A. We obtain some hereditary properties of φ-injectivity for certain classes of Banach modules related to closed ideals. These results allow us to study φ-injectivity of certain Banach A-modules in commutative case, specially ℓ 1 -semilattice algebras. As an application, we give an example of a non-injective Banach module which is φ-injective for each character φ.2010 Mathematics Subject Classification. Primary 46M10 Secondary 43A20, 46H25.

Abstract. Let A be a Banach algebra and X be a Banach A-bimodule. We introduce and study the notions of n-multipliers and approximate local nmultipliers by generalizing the classical concept of multipliers from A into X. As an algebraic result, we construct a Banach algebra consisting of nmultipliers on A and under some mild conditions, we give a nice relation of this algebra with n-homomorphisms from A into C.