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Spectral Symmetry in II_1 Factors

Sang Hyun Kim·Gabriel Nagy
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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 $t\longmapsto -t$. 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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Sang Hyun Kim, Gabriel Nagy. 2004-09-06. Spectral Symmetry in II_1 Factors. https://arxiv.org/abs/math/0408275

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