W*-Bundles

QA Mathematics

Evington, Samuel ; Engineering and Physical Sciences Research Council (EPSRC) ; White, Stuart

University:University of Glasgow

Department:School of Mathematics and Statistics

关键词: W*-Bundles, operator algebras, C*-algebras, von Neumann algebras, subfactors, classification of C*-algebras.;   

Others  :  http://theses.gla.ac.uk/8650/1/2018EvingtonPhD.pdf

来源: University of Glasgow

【 摘 要 】

This thesis collates, extends and applies the abstract theory of W*-bundles. Highlightsinclude the standard form for W*-bundles, a bicommutant theorem for W*-bundles, andan 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 ispresented, and propertygamma and the McDuff property for W*-bundles are investigated thoroughly.Ozawa's Triviality Theorem is applied to some new examples such as the strictclosures of Villadsen algebras and non-trivial C(X)-algebras. The solution to the TrivialityProblem 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. Asub-W*-bundle encapsulates a tracially continuous family of subfactors in a singleobject. The basic construction and the Jones tower are generalised to this new setting and the first examples of sub-W*-bundles are constructed.