Isometries on symmetric spaces associated with semi-finite von Neumann algebras

Isometries on Banach spaces of measurable functions can typically be characterized as weighted composition operators. In the non-commutative setting, isometries between symmetric spaces (of trace-measurable operators) can often be described in terms of a Jordan ✽-homomorphism (which may be considered a non-commutative composition operator) weighted by a partial isometry and/or a positive operator. In this thesis we describe the structures of isometries on various (non-commutative) symmetric spaces associated with semi-finite von Neumann algebras. This is achieved by extending certain results from the finite setting to the semi-finite setting, exploring the applicability of disjointness-preserving techniques in generalizations of Lₚ-spaces, and developing characterizations of extreme points in a certain class of Lorentz spaces and in various types of Orlicz spaces.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2017

Author dc:creator

• De Jager, Pierre

Advisors dc:contributor.advisor

• Conradie, Jurie J
• Martin, R T W

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/25167

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/25167