Methods of Perturbation Theory

Abstract

Though not every pair of bounded self-adjoint operators X,Y ε L (H), satisfying [X, Y] ε C₁ (and possibly i[X,Y] ≥ 0) fits into the classical scheme of perturbation theory, namely X - Y is not necessarily trace-class, the existence of the singular integral model for the couple (X,Y) offers some analogies and even an effective way of applying perturbation theoretical methods to the study of such a pair of operators. This idea, due to Carey and Pincus, will be developed starting with the next chapter.