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dc.contributor.advisorYu, Guoliang
dc.creatorChung, Yeong Chyuan
dc.date.accessioned2018-02-05T16:49:14Z
dc.date.available2018-02-05T16:49:14Z
dc.date.created2017-08
dc.date.issued2017-05-24
dc.date.submittedAugust 2017
dc.identifier.urihttp://hdl.handle.net/1969.1/165723
dc.description.abstractThis dissertation can be said to fall under the broad theme of computability of K-theory of Lp operator algebras (and perhaps more general Banach algebras). The first part of the dissertation is about a variant of K-theory known as quantitative K-theory, which has been defined for C*_-algebras and applied in a number of situations. Our goal is to extend the theory to a larger class of Banach algebras so that it becomes applicable to Lp operator algebras and thus a tool for investigating an Lp version of the Baum-Connes conjecture. We develop the general framework for this theory, culminating in a version of the controlled Mayer-Vietoris sequence that has featured prominently in existing applications in the C*_-algebra setting. In the second part of the dissertation, we study the Lp version of one of these applications.This application involves the notion of dynamic asymptotic dimension, which is a notion of dimension associated to group actions on spaces (and more generally to groupoids). In the C*_-algebra setting, the work of Guentner-Willett-Yu showed that when a group G acts on a compact space X with finite dynamic asymptotic dimension, the Baum-Connes conjecture with coefficients in C(X) holds for the group G. We will formulate an Lp version of the Baum-Connes conjecture with coefficients and show that under the same assumption, the Lp Baum-Connes conjecture with coefficients in C(X) holds for the group G. As a consequence, the K-theory of the Lp reduced crossed product of C(X) by G does not depend on p if the action has finite dynamic asymptotic dimension.en
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.subjectK-theoryen
dc.subjectBanach algebraen
dc.subjectLp operator algebraen
dc.subjectdynamic asymptotic dimensionen
dc.titleQuantitative K-theory for Banach Algebras and Its Applicationsen
dc.typeThesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorTexas A & M Universityen
thesis.degree.nameDoctor of Philosophyen
thesis.degree.levelDoctoralen
dc.contributor.committeeMemberXie, Zhizhang
dc.contributor.committeeMemberDykema, Kenneth Jay
dc.contributor.committeeMemberDahm, Paul Fred
dc.type.materialtexten
dc.date.updated2018-02-05T16:49:14Z
local.etdauthor.orcid0000-0001-5750-3424


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