W*-bundles

• Main Author: Evington, Samuel
• Published: University of Glasgow 2018
• Subjects: QA Mathematics
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.732765

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.