Perturbation bounds for angular sectors of spectra of unbounded operators

Abstract

Let A and $$\tilde{A}$$ be linear unbounded in general operators on a Hilbert space. We consider the following problem: let the spectrum of A lie in some angular sector. In what sector the spectrum of $$\tilde{A}$$ lies, if A and $$\tilde{A}$$ are sufficiently “close”? Illustrative examples are also presented.