Operators reversing orthogonality in normed spaces

Abstract

We consider linear operators $T: X \to X$ on a normed space $X$ which reverse orthogonality, i.e., satisfy the condition $$x \bot y \quad \Longrightarrow \quad Ty \bot Tx, \qquad x,y \in X,$$ where $\bot$ stands for Birkhoff orthogonality.