LINEAR ORTHOGONALITY PRESERVERS OF STANDARD OPERATOR ALGEBRAS

Abstract

In 2003, Araujo and Jarosz showed that every bijective linear map $\theta: A \to B$ between unital standard operator algebras preserving zero products in two ways is a scalar multiple of an inner automorphism. Later in 2007, Zhao and Hou showed that similar results hold if both $A,B$ are unital standard algebras on Hilbert spaces and $\theta$ preserves range or domain orthogonality. In particular, such maps are automatically bounded. In this paper, we will study linear orthogonality preservers in a unified way. We will show that every surjective linear map between standard operator algebras preserving range/domain orthogonality carries a standard form, and is thus automatically bounded.