SPECTRUM LOCALIZATION OF A PERTURBED OPERATOR IN A STRIP AND APPLICATIONS

Let A and (A) over tilde be bounded operators in a Hilbert space. We consider the following problem: let the spectrum of A lie in some strip. In what strip the spectrum of (A) over tilde lies if A and (A) over tilde are "close"? Applications of the obtained results to integral operators and matrices are also discussed. In addition, we apply our perturbation results to approximate the spectral strip of a Hilbert-Schmidt operator by the spectral strips of finite matrices.