Coburn Type Operators And Compact Perturbations On The Hilbert Space

In this thesis,we first review some results of approximation of operators defined on com-plex separable infinite dimensional Hilbert space H.They are concerned with such those problems:When an operator possesses one given property by arbitrary small compact per-turbations.When one given property is stabilized under given perturbations,such as com-muting nilpotent perturbations,commuting finite rank perturbations,compact perturba-tions and small compact perturbations et al.On this basis,we define Coburn type properties of operators.Especially,we call operatorhas Coburn property if either ker(-)={0}or ker(-)~*={0}for all complex number?C.We establish for a bounded linear operatorseveral sufficient and necessary conditions for which there exists a small enough compact operatorsuch that+possesses given Coburn type property.And also we characterize the stability of Coburn type properties under small compact perturbations.