Perturbations of Finite Dimensional and Compact Operators
Michael I. Gil’ · 2021
This chapter is devoted to spectrum perturbations of finite-dimensional and compact operators. By the multiplicative structure of the resolvent of a finite dimensional operator, bounds for eigenvalues and for the determinant of an arbitrary finite matrix are derived. The chapter is also devoted to approximations of a compact operator by finite dimensional operators. It examines spectrum perturbations of Hilbert-Schmidt operators, and investigates compact operators with a finite trace. The chapter deals with operators whose powers are Hilbert-Schmidt operators, and also examines the operators belonging to the Neumann-Schatten ideals. By the multiplicative structure of the resolvent of a compact operator with a finite trace, bounds for eigenvalues are derived.