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