Semi-Fredholm operators and pure contractions in Hilbert space

Abstract

In Kaufman (Proc Amer Math Soc 72: 531–534, 1978) proved that the function defined by maps the set $$\fancyscript{C}_{0}(H)$$ of all pure contractions one-to-one onto the set $$\fancyscript{C}(H)$$ of all closed and densely defined linear operators on Hilbert space . In this paper, we gives some further properties of , we establish the semi-Fredholmness and Fredholmness of unbounded operators in terms of bounded pure contractions, and we apply this results to an 2 2 upper triangular operator matrices. An application to linear delay differential equation is given.