THE ϕ-INNER DERIVATIONS AND THE GENERALIZED ϕ-DERIVATIONS ON BANACH ALGEBRAS

Nguyen Huu Quang; Dinh Thi Xinh

Nguyen Huu Quang
Dinh Thi Xinh

Keywords: Banach algebra, derivation, inner derivation

Abstract

This paper presents some properties of the ϕ-derivations and the generalized ϕ-derivations from a Banach algebra A into a Banach algebra B. The innerness, one of the most attracting aspect of the derivations on Banach algebras, is also considered. The last sections of this work is discussion about the ϕ-homomorphisms from A into B and some continuous properties of the generalized ϕ-derivations.