Coburn Type Operators and Compact Perturbations

A bounded linear operator T acting on a Hilbert space is called Coburn operator if ker(T-λ) = {0} or ker(T-λ)*= {0} for each λ∈ C. In this paper, the authors define other Coburn type properties for Hilbert space operators and investigate the compact perturbations of operators with Coburn type properties. They characterize those operators for which has arbitrarily small compact perturbation to have some fixed Coburn property.Moreover, they study the stability of these properties under small compact perturbations.