The Hahn-Banach Separation Theorem in Free Convexity
type: CreativeWork
description: This thesis presents and develops theorems on separation in the context of free convexity and matrix convex sets. After presenting a proof of the Hahn-Banach Separation Theorem, the main work in this thesis is a treatment of the Effros-Winkler Hahn-Banach Separation Theorem in the setting of matrix convex sets. This result is subsequently interpreted as a theorem concerning noncommutative sets in free analysis. Lastly, a new and complete characterization (in terms of liner pencils) of the matrix convex hull of a g-tuple of complex matrices is established.
abstract: This thesis presents and develops theorems on separation in the context of free convexity and matrix convex sets. After presenting a proof of the Hahn-Banach Separation Theorem, the main work in this thesis is a treatment of the Effros-Winkler Hahn-Banach Separation Theorem in the setting of matrix convex sets. This result is subsequently interpreted as a theorem concerning noncommutative sets in free analysis. Lastly, a new and complete characterization (in terms of liner pencils) of the matrix convex hull of a g-tuple of complex matrices is established.
author: Cui, Bo
language: en
date published: 2015-12
date modified: 2026-07-24T04:03:32Z
provider: University of Regina
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Faculty of Graduate Studies and Research, University of Regina

PropertyValue
property ID: Handle
value: https://hdl.handle.net/10294/6853

PropertyValue
property ID: DOI
value: 10.82465/4136