Topics regarding close operator algebras

QA Mathematics

Dickson, Liam ; White, Stuart

University:University of Glasgow

Department:School of Mathematics and Statistics

关键词: Operator algebras, perturbations;   

Others  :  http://theses.gla.ac.uk/6276/1/2014DicksonPhD.pdf

来源: University of Glasgow

【 摘 要 】

In this thesis we focus on two topics. For the first we introduce a row version of Kadison andKastler's metric on the set of C*-subalgebras of B(H). By showing C*-algebras have row length (inthe sense of Pisier) of at most two we show that the row metric is equivalent to the original Kadison-Kastler metric. We then use this result to obtain universal constants for a recent perturbation resultof Ino and Watatani, which states that succiently close intermediate subalgebras must occur assmall unitary perturbations, by removing the dependence on the structure of inclusion.Roydor has recently proved that injective von Neumann algebras are Kadison-Kastler stable ina non-self adjoint sense, extending seminal results of Christensen. We prove a one-sided version,showing that an injective von Neumann algebra which is nearly contained in a weak*-closed non-selfadjoint algebra can be embedded by a similarity close to the natural inclusion map. This theoremcan then be used to extend results of Cameron et al. by demonstrating Kadison-Kastler stabilityof certain crossed products in the non self-adjoint setting. These crossed products can be chosento be non-amenable.