Compact and finite rank perturbations of linear relations in Hilbert spaces

Abstract. For closed linear operators or relations A and B acting between Hilbert spaces H and K the concepts of compact and finite rank perturbations are introduced with the help of the orthogonal projections PA and PB in H©K onto A and B. Various equivalent characterizations for such perturbations are proved and it is shown that these notions are a natural generalization of the usual concepts of compact and finite rank perturbations.