Veeramani, S and D, Sukumar
(2018)
CONTINUITY OF CONDITION SPECTRUM AND ITS LEVEL SET IN
BANACH ALGEBRA.
PhD thesis, Indian Institute of Technology hyderabad.
Abstract
For 0 < � < 1 and a Banach algebra element a, this thesis aims to establish
the results related to continuity of condition spectrum and its level set correspondence
at (�; a). Here we propose a method of study to achieve the continuity. We
first identify the Banach algebras at which the interior of the level set of condition
spectrum is empty and then we obtain the continuity results.
This thesis consists of four chapters. Chapter 1 contains all the prerequisites
which are crucial for the development of the thesis. In particular, this chapter
has a quick review of the basic properties of spectrum, condition spectrum, upper
and lower hemicontiuous correspondences. We also concentrate on analytic vector
valued maps and generalized maximum modulus theorem for them.
For an element a in A, Chapter 2 has the results related to interior of the level of
set of the condition spectrum of a. At first, we focus on 1
[error in script]
| IITH Creators: |
| IITH Creators | ORCiD |
|---|
| D, Sukumar | UNSPECIFIED |
|
| Item Type: |
Thesis
(PhD)
|
| Uncontrolled Keywords: |
condition spectrum, vector valued analytic maps, maximum modulus principle, upper and lower hemicontinuous correspondence, |
| Subjects: |
Mathematics |
| Divisions: |
Department of Mathematics |
| Depositing User: |
Team Library
|
| Date Deposited: |
25 Jul 2018 11:19 |
| Last Modified: |
25 Jul 2018 11:23 |
| URI: |
http://raiithold.iith.ac.in/id/eprint/4309 |
| Publisher URL: |
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| Related URLs: |
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