2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72236A 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.38 pages, AMSLaTeXOperator AlgebrasFunctional Analysis47L30text