(1) Department of Mathematics and Applied Mathematics, University of Pretoria, 0002 Pretoria, South Africa
Abstract:
In this paper we obtain a number of interesting results on the connection
that exists between the essential lower bound of an element in a von
Neumann algebra and its Fredholm properties. These connections lead to an
extension of a well-known perturbation theorem on Fredholm operators of
index zero. Finally we obtain for special cases necessary and sufficient conditions
for elements in the closure of the group of invertible elements to be
essentially topological divisor of zero