Maps preserving the Banach operator pairs on operator algebras

Document Type: Research Paper

Author

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

10.22072/wala.2019.103404.1217

Abstract

Let $\mathcal{B(X)}$ be the algebra of all linear bounded operators on a Banach
space $\mathcal{X}$ and $\phi:\mathcal{B(X)}\longrightarrow \mathcal{B(X)}$ be an additive bijective map preserving the Banach operator pairs, in both directions. In this paper, it is shown that for every $A \in \mathcal{B(X)}$‎ and ‎$x \in \mathcal{X}$, there are scalars  $\alpha‎ , ‎\beta \in \mathbb{C}$‎ such that $\phi(A)x=\alpha x+\beta Ax$.

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