Minimum Moduli in Von Neumann Algebras

Abstract

In this paper we answer a question raised in [12] in the affirmative, namely that the essential minimum modulus of an element in a von Neumann algebra, relative to any norm closed two-sided ideal, is equal to the minimum modulus of the element perturbed by an element from the ideal. As a corollary of this result, we extend some basic perturbation results on semi-Fredholm elements to a von Neumann algebra setting. We can characterize the semi-Fredholm elements in terms of the points of continuity of the essential minimum modulus function.
Mathematics Subject Classification (2000): 46L
Keywords: algebra, selfadjoint operator algebras, Fredholm theory, von Neumann algebra, minimum modulus, semi-Fredholm

Quaestiones Mathematicaes 24 (4) 2001, 493–500