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.