On right (left) θ-centralizers on Banach algebras

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Science, University of Kurdistan, P.O. Box 416, Sanandaj, Kurdistan, Iran.

Abstract

Let A be a Banach algebra with unity 1, and θ : A → A be an continuous automorphism. In this paper we characterize
a continuous linear map T : A → A which satisfies one of the following conditions:
a, b ∈ A, ab = w =⇒ θ(a)T(b) = T(w),
a, b ∈ A, ab = w =⇒ T(a)θ(b) = T(w),
or a, b ∈ A, ab = w =⇒ θ(a)T(b) = T(a)θ(b) = T(w) , where w ≠ 0 is a left (right) separating point of A.

Keywords


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