Spectral Symmetry in II_1 Factors

Details Spectral Symmetry in II_1 Factors Spectral Symmetry in II_1 Factors

2004-08-20

arxiv.org/abs/math/0408275v2

Mathematics

Operator Algebras

38 pages, AMSLaTeX

Scientific paper

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 $t\longmapsto -t$. 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.

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