Author: Nurulla Azamov
Azamov, Nurulla, 2008 Spectral shift function in von Neumann algebras, Flinders University, School of Computer Science, Engineering and Mathematics
Terms of Use: This electronic version is (or will be) made publicly available by Flinders University in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. You may use this material for uses permitted under the Copyright Act 1968. If you are the owner of any included third party copyright material and/or you believe that any material has been made available without permission of the copyright owner please contact copyright@flinders.edu.au with the details.
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.
Keywords: spectral shift function,spectral flow,Dixmier trace
Subject: Engineering thesis
Thesis type: Doctor of Philosophy
Completed: 2008
School: School of Computer Science, Engineering and Mathematics
Supervisor: Dr. F. Sukochev