Return to search

Approximately Inner Automorphisms of von Neumann Factors

Through von Neumann's reduction theory, the classification of injective von Neumann algebras acting on separable Hilbert spaces translates into the classification of injective factors. In his proof of the uniqueness of the injective type II₁ factor, Connes showed an alternate characterization of the approximately inner automorphisms of type II₁ factors. Moreover, he conjectured that this characterization could be extended to all types of factors acting on separable Hilbert spaces. In this thesis, we present a general toolbox containing the basic notions needed to study von Neumann algebras, before describing our work concerning Connes' conjecture in the case of type IIIλ factors. We have obtained partial results towards the proof of a modified version of this conjecture.

Identiferoai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/41879
Date15 March 2021
CreatorsGagnon-Bischoff, Jérémie
ContributorsGiordano, Thierry
PublisherUniversité d'Ottawa / University of Ottawa
Source SetsUniversité d’Ottawa
LanguageEnglish
Detected LanguageEnglish
TypeThesis
Formatapplication/pdf

Page generated in 0.0022 seconds