On the Essential Lower Bound of Elements in von Neumann Algebras

In this paper we obtain a number of interesting results on the connectionthat exists between the essential lower bound of an element in a vonNeumann algebra and its Fredholm properties. These connections lead to anextension of a well-known perturbation theorem on Fredholm operators ofindex zero. Finally we obtain for special cases necessary and sufficient conditionsfor elements in the closure of the group of invertible elements to beessentially topological divisor of zero