Spectral Symmetry in II_1 Factors

Abstract

A self-adjoint element in a finite AW*-factor is spectrally symmetric, if its spectral measure under the quasitrace is invariant under the change of variables $t⟼-t$. We show that if $\mathcal{A}$ is an AW*-factor of type II_1, a self-djoint element in $\mathcal{A}$, without full support, has quasitrace zero, if and only if it can be written as a sum of at most three commuting spectrally symmetric elements.

38 pages, AMSLaTeX

References in corpus (1)

• Abelian self-commutators in finite factors