This article is cited in 1 paper

Maps preserving the coincidence points of operators

R. Hosseinzadeh

Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P. O. Box 47416-1468, Babolsar, Iran

Abstract: Let $\mathcal{B(X)}$ be the algebra of all bounded linear operators on a Banach space $\mathcal{X}$ with $\dim \mathcal{X} \geqslant 2$. In this paper, we describe surjective maps $\phi: \mathcal{B(X)}\to\mathcal{B(X)}$ preserving the coincidence points of operators, i.e., $C(A,B)=C(\phi(A),\phi(B))$, for every $A, B \in \mathcal{B(X)}$, where $C(A,B)$ denotes the set of all coincidence points of two operators $A$ and $B$.

Keywords and phrases: preserver problem, coincidence points.

MSC: 46J10, 47B48

Received: 28.04.2020

Language: English

DOI: 10.32523/2077-9879-2021-12-3-42-45

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