Topics regarding close operator algebras

Dickson, Liam (2014) Topics regarding close operator algebras. PhD thesis, University of Glasgow.

Abstract

In this thesis we focus on two topics. For the first we introduce a row version of Kadison and
Kastler's metric on the set of C*-subalgebras of B(H). By showing C*-algebras have row length (in
the 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 result
of Ino and Watatani, which states that succiently close intermediate subalgebras must occur as
small unitary perturbations, by removing the dependence on the structure of inclusion.
Roydor has recently proved that injective von Neumann algebras are Kadison-Kastler stable in
a 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-self
adjoint algebra can be embedded by a similarity close to the natural inclusion map. This theorem
can then be used to extend results of Cameron et al. by demonstrating Kadison-Kastler stability
of certain crossed products in the non self-adjoint setting. These crossed products can be chosen
to be non-amenable.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Operator algebras, perturbations
• Subjects: Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Supervisor's Name: White, Dr. Stuart
• Date of Award: 2014
• Depositing User: Mr Liam Dickson
• Unique ID: glathesis:2014-6276
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 28 Apr 2015 09:43
• Last Modified: 04 May 2015 14:04
• URI: https://theses.gla.ac.uk/id/eprint/6276