Abelian self-commutators in finite factors

Abstract

An abelian self-commutator in a C*-algebra $\mathcal{A}$ is an element $A$ that can be written as $A=X^{\ast }X-X{X}^{\ast }$, with $X\in \mathcal{A}$ such that $X^{\ast }X$ and $X{X}^{\ast }$ commute. It is shown that, given a finite AW*-factor $\mathcal{A}$, there exists another finite AW*-factor $\mathcal{M}$ of same type as $\mathcal{A}$, that contains $\mathcal{A}$ as an AW*-subfactor, such that any self-adjoint element $X\in \mathcal{M}$ of quasitrace zero is an abelian self-commutator in $\mathcal{M}$.

12 pages, AMSLaTeX

Cited by in corpus (1)

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