Hankel operators in the perturbation theory of unitary and self-adjoint operators (Q1072077)

The author introduces a new technique in the following questions of the perturbation theory of unitary and self-adjoint operators: the representation of \(\phi\) (B)-\(\phi\) (A) in the term of operator integrals, the representation of the trace of \(\phi\) (B)-\(\phi\) (A) in the term of so-called spectral shift function, the differentiability of the mapping \(A\mapsto \phi (A).\) This technique is based on the metric properties of some Hankel operators.