A Uniform Commutator Bound in Finite Von Neumann Algebras
Let $\mathcal{M}$ be a finite von Neumann algebra with normalized center-valued trace $T_\mathcal{M}$. We prove that every $A\in\mathcal{M}$ with $T_\mathcal{M}(A)=0$ admits a representation $A=BC−CB$, where $B,C\in\mathcal{M}$ satisfy $\lVert B\rVert\lVert C\rVert\leq K\lVert A\rVert$ for an absolute constant $K$ independent of $\mathcal{M}$.
