Operators reversing orthogonality in normed spaces

Document Type: Original Article

Author

Pedagogical University of Cracow

Abstract

We consider linear operators $T\colon X\to X$ 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.

Keywords