ABSTRACT
This chapter is devoted to relatively bounded perturbations of unbounded operators defined on a tensor product of Hilbert spaces. It introduces a class of operator-valued functions on a tensor product of Hilbert spaces. The chapter investigates spectrum perturbations of unbounded operators on the tensor product by the norm estimations for the operator-valued functions. A bound is obtained for eigenvalues of a second order nonselfadjoint matrix differential operator on a segment. A bound is established for the spectrum of a high order matrix differential operator on the real axis. The chapter also investigates the spectrum of a periodic matrix differential operator. It considers separately the cases of: a finite interval, the semi-axis, and the whole axis. The chapter presents the well-known asymptotical estimates for scalar second order differential operators.
