Gleason solutions and canonical models for row contractions

This thesis extends the deBranges-Rovnyak model for completely non-coisometric (CNC) contractions to the setting of row contractions from several copies of a Hilbert space into itself. It is shown that a large class of of row contractions (including all CNC row contractions with commuting components) can be represented as extremal Gleason solutions in the de Branges-Rovnyak space associated to a contractive multiplier between vector-valued Drury-Arveson spaces. Here, a Gleason solution is the appropriate several-variable analogue of the adjoint of the restricted backward shift. Given such a row contraction T, the corresponding multiplier bT , that is, the characteristic function of T, is shown to be unitary invariant. We further characterise a natural sub-class of row contractions for which it is a complete unitary invariant.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2017

Author dc:creator

• Ramanantoanina, Andriamanankasina

Advisor dc:contributor.advisor

• Martin, Robert T W

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/25491

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/25491