D-class Operators And Compact Perturbations

A bounded linear operator T acting on a Hilbert space is called D1-class operator if dim ker(T-A)=dim ker(T-λ)*=∞ for each λ∈iso σ(T);T is called D2-class operator if ran(T-λ)is not closed for each λ∈σ(T).In this paper,we investigate the compact perturbations of operators with D1-class and D2-class properties.We characterize those operators for which has arbitrarily small compact perturbations to have D-class property.Also,we study the stability of these properties under small compact perturbations.