On maps preserving skew symmetric operators

Abstract

Given a conjugation $C$ on a separable complex Hilbert space $H$, a bounded linear operator $T$ on $H$ is said to be $C$-skew symmetric if $CTC=-T^*$. This paper describes the maps, on the algebra of all bounded linear operators acting on $H$, that preserve the difference of $C$-skew symmetric operators for every conjugation $C$ on $H$.