On regularizers of unbounded linear operators in Banach spaces

Abstract

Regularizers of densely defined unbounded linear operators in Banach spaces and their applications to spectral theory are considered. Necessary and sufficient conditions in terms of regularizer properties for an unbounded operator T to have discrete spectrum are obtained. In the case where T has a self-adjoint regularizer in some Schatten--von Neumann ideals, asymptotic properties of the eigenvalues are investigated; in particular, it is shown that the eigenvalues of T asymptotically belong to some angle in the complex plane. Bibliography: 16 titles.