On Indefinite Cases of Operator Identities Which Arise in Interpolation Theory
James Rovnyak, Lev Sakhnovich · Birkhäuser Basel eBooks · 2007
Operator identities involving nonnegative selfadjoint operators play a fundamental role in interpolation theory and its applications. The theory is generalized here to selfadjoint operators whose negative spectra consist of a finite number of eigenvalues of finite total multiplicity. It is shown that such identities are closely associated with generalized Nevanlinna functions by means of the Kreĭn-Langer integral representation. The Potapov fundamental matrix inequality is generalized to this situation, and it is used to formulate and solve an operator interpolation problem analogous to the definite case.