Maps Preserving the Coincidence Points of Operators

Abstract

Let B(X) be the algebra of all bounded linear operators on a Banach space X with dimX ≥ 2. In this paper, we describe surjective maps φ : B(X) → B(X) preserving the coincidence points of operators, i.e., C(A,B) = C(φ(A), φ(B)), for every A,B ∈ B(X), where C(A,B) denotes the set of all coincidence points of two operators A and B.