 Abstract | The main subsect of this thesis is the theory of Lifshits-Krein spectral shift function in semifinite von Neumann algebras and its connection with the theory of spectral flow.
Main results are an analogue of the Krein trace formula for semifinite von Neumann algebras, the semifinite analogue of the Birman-Solomyak spectral averaging formula, a connection between the spectral shift function and the spectral flow and a Lidskii type formula for Dixmier traces. In particular, it is established that in the case of operators with compact resolvent, the spectral shift function and the spectral flow are identical notions. |
