Unitarily invariant norms on finite von Neumann algebras

Abstract

We give a characterization of all the unitarily invariant norms on a finite von Neumann algebra acting on a separable Hilbert space. The characterization is analogous to von Neumann’s characterization for the \(n\times n\) complex matrices and the characterization in Fang et al. (J Funct Anal 255(1):142–183, 2008) for \(II_{1}\) factors.