dc.contributor.advisor | Yu, Guoliang | |
dc.creator | Chung, Yeong Chyuan | |
dc.date.accessioned | 2018-02-05T16:49:14Z | |
dc.date.available | 2018-02-05T16:49:14Z | |
dc.date.created | 2017-08 | |
dc.date.issued | 2017-05-24 | |
dc.date.submitted | August 2017 | |
dc.identifier.uri | https://hdl.handle.net/1969.1/165723 | |
dc.description.abstract | This 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.mimetype | application/pdf | |
dc.language.iso | en | |
dc.subject | K-theory | en |
dc.subject | Banach algebra | en |
dc.subject | Lp operator algebra | en |
dc.subject | dynamic asymptotic dimension | en |
dc.title | Quantitative K-theory for Banach Algebras and Its Applications | en |
dc.type | Thesis | en |
thesis.degree.department | Mathematics | en |
thesis.degree.discipline | Mathematics | en |
thesis.degree.grantor | Texas A & M University | en |
thesis.degree.name | Doctor of Philosophy | en |
thesis.degree.level | Doctoral | en |
dc.contributor.committeeMember | Xie, Zhizhang | |
dc.contributor.committeeMember | Dykema, Kenneth Jay | |
dc.contributor.committeeMember | Dahm, Paul Fred | |
dc.type.material | text | en |
dc.date.updated | 2018-02-05T16:49:14Z | |
local.etdauthor.orcid | 0000-0001-5750-3424 | |