The Jacobson radical of semicrossed products of the disk algebra

Thumbnail Image
Date
2012-01-01
Authors
Khemphet, Anchalee
Major Professor
Advisor
Justin Peters
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Altmetrics
Authors
Research Projects
Organizational Units
Organizational Unit
Journal Issue
Is Version Of
Versions
Series
Department
Mathematics
Abstract

In this thesis, we characterize the Jacobson radical of the semicrossed product of the disk algebra by an endomorphism which is defined by the composition with a finite Blaschke product. Precisely, the Jacobson radical is the set of those whose 0th Fourier coefficient is identically zero and whose kth Fourier coefficient vanishes on the set of recurrent points of a finite Blaschke product. Moreover, if a finite Blaschke product is elliptic, i.e., it has a fixed point in the open unit disc, then the Jacobson radical coincides with the set of quasinilpotent elements.

Comments
Description
Keywords
Citation
Source
Subject Categories
Copyright
Sun Jan 01 00:00:00 UTC 2012