2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61467We introduce notation Q(1) * ... * Q(n) * L(F_r)$ for von Neumann algebra II_1 factors where $r$ is allowed to be negative. This notation is defined by rescalings of free products of II_1 factors, and is proved to be consistent with known results and natural operations. We also give two statements which we prove are equivalent to isomorphism of free group factors.5 pagesOperator Algebras46L54text