Perturbations of Semi-Fredholm Operators in Locally Convex Spaces

This present article is a detailed version of the lecture I gave at the International Seminar on Functional Analysis, Holomorphy and Approximation Theory in Rio de Janeiro in August 1979. It is intended as a survey of a new concept of a duality theory for closed linear operators in locally convex spaces. This theory is successfully applied to perturbation problems in locally convex spaces and to linear partial differential operators (LPDO’s) in local weighted Sobolev spaces and in C^∞(Ω).