2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62782We investigate maximal abelian subalgebras (masas) in separably acting type $II_1$ factors. We use the notion of distance between masas which we introduced in an earlier paper in this archive, OA/0107075. The main result of the paper is to show that for any unitary u and a masa A, the distance between A and uAu* is comparable to the distance in 2-norm from u to the unitary normalizer N(A) of A. In qualitative terms, this says that a unitary almost normalizes A if and only if it is close to a normalizing unitary. Inequalities in the paper make this statement quantitatively precise. As a consequence, all singular masas in separably acting type $II_1$ factors are $α$-strongly singular, as defined in the above referenced paper, for a universal value of $α$.latex file, 29 pagesOperator Algebras46L10; 46L35text