Approximately Inner Automorphisms of von Neumann Factors

Abstract

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.