W*-Bundles

Evington, Samuel (2018) W*-Bundles. PhD thesis, University of Glasgow.

Abstract

This thesis collates, extends and applies the abstract theory of W*-bundles. Highlights
include the standard form for W*-bundles, a bicommutant theorem for W*-bundles, and
an investigation of completions, ideals, and quotients of W*-bundles.
The Triviality Problem, whether all W*-bundles with fibres isomorphic to the hyperfinite II_1 factor are trivial, is central to this thesis. Ozawa's Triviality Theorem is
presented, and property gamma and the McDuff property for W*-bundles are investigated thoroughly.
Ozawa's Triviality Theorem is applied to some new examples such as the strict
closures of Villadsen algebras and non-trivial C(X)-algebras. The solution to the Triviality
Problem in the locally trivial case, obtained by myself and Pennig, is included.
A theory of sub-W*-bundles is developed along the lines of Jones' subfactor theory. A
sub-W*-bundle encapsulates a tracially continuous family of subfactors in a single
object. The basic construction and the Jones tower are generalised to this new setting and the first examples of sub-W*-bundles are constructed.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: W*-Bundles, operator algebras, C*-algebras, von Neumann algebras, subfactors, classification of C*-algebras.
• Subjects: Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Funder's Name: Engineering and Physical Sciences Research Council (EPSRC), Engineering and Physical Sciences Research Council (EPSRC), Engineering and Physical Sciences Research Council (EPSRC), Engineering and Physical Sciences Research Council (EPSRC)
• Supervisor's Name: White, Prof. Stuart
• Date of Award: 2018
• Depositing User: Mr Samuel Evington
• Unique ID: glathesis:2018-8650
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 03 Jan 2018 10:26
• Last Modified: 19 Jan 2018 09:51
• URI: https://theses.gla.ac.uk/id/eprint/8650