von Neumann algebra preduals satisfy the linear biholomorphic property

Abstract

We prove that for every JBW${}^{\ast }$-triple $E$ of rank $>1$, the symmetric part of its predual reduces to zero. Consequently, the predual of every infinite dimensional von Neumann algebra $A$ satisfies the linear biholomorphic property, that is, the symmetric part of $A_{\ast }$ is zero. This solves a problem posed by M. Neal and B. Russo in [Mathematica Scandinavica, to appear]