Paper's Title:

Automatic Continuity of Generalized Derivations in Certain *-Banach Algebras

Author(s):

M. Aboulekhlef, Y. Tidli and M. Belam

Laboratory of Applied Mathematics and Information and Communication Technology Polydisciplinary
Faculty of Khouribga University of Sultan Moulay Slimane
Morocco.
E-mail: aboulekhlef@gmail.com y.tidli@gmail.com m.belam@gmail.com

Abstract:

Consider the map φ of the Banach algebra Β in Β, if there exists a derivation δ of Β in Β so that for every  x, y ∈ Β , φ(xy) =φ(x)y+xδ(y) . φ is called a generalized derivation of Β. In [9], Bresar introduced the concept of generalized derivations. We prove several results about the automatic continuity of generalized derivations on certain Banach algebras.

Paper's Title:

The Automatic Continuity of N-Homomorphisms in Certain *-Banach Algebras

Author(s):

M. Aboulekhlef, Y. Tidli

Laboratory of Applied Mathematics and Information and Communication Technology
Polydisciplinary Faculty of Khouribga
University of Sultan Moulay Slimane
Morocco.
E-mail: aboulekhlef@gmail.com y.tidli@gmail.com

Abstract:

In this study, we prove the automatic continuity of surjective n-homomorphism between complete p-normed algebras. We show also that if Α and Β are complete *-p-normed algebras, Β is *simple and ψ: Α → Β is a surjective n-homomorphism under certain conditions, then ψ is continuous.

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