Graph subspaces and the spectral shift function. (English) Zbl 1074.47007
Authors’ abstract: “We obtain a new representation for the solution to the operator Sylvester equation in the form of a Stieltjes operator integral. We also formulate new sufficient conditions for the strong solvability of the operator Riccati equation that ensures the existence of reducing graph subspaces for block operator matrices. Next, we extend the concept of the Lifshits-Krein spectral shift function associated with a pair of self-adjoint operators to the case of pairs of admissible operators that are similar to self-adjoint operators. Based on this new concept, we express the spectral shift function arising in a perturbation problem for block operator matrices in terms of the angular operators associated with the corresponding perturbed and unperturbed eigenspaces.”
Reviewer: Costică Moroşanu (Iaşi)
MSC:
47A55 | Perturbation theory of linear operators |
47A10 | Spectrum, resolvent |
47A40 | Scattering theory of linear operators |
47B25 | Linear symmetric and selfadjoint operators (unbounded) |
47B44 | Linear accretive operators, dissipative operators, etc. |
47A20 | Dilations, extensions, compressions of linear operators |