Von Neumann Algebra Preduals Satisfy the Linear Biholomorphic Property

Abstract

We prove that for every $\mathrm{JBW}^*$-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 $A_*$ is zero.