CONTINUITY OF CONDITION SPECTRUM AND ITS LEVEL SET IN BANACH ALGEBRA

Veeramani, S and D, Sukumar (2018) CONTINUITY OF CONDITION SPECTRUM AND ITS LEVEL SET IN BANACH ALGEBRA. PhD thesis, Indian Institute of Technology hyderabad.

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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

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IITH Creators:
IITH CreatorsORCiD
D, SukumarUNSPECIFIED
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://raiith.iith.ac.in/id/eprint/4309
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