Level sets of (p,e-p)outer generalized pseudo spectrum

D, Sukumar and Veeramani, S (2017) Level sets of (p,e-p)outer generalized pseudo spectrum. Journal of Analysis. pp. 1-14. ISSN 0971-3611 (In Press)

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Abstract

Let A be a complex Banach algebra with unit e. Let p be a non trivial idempotent element in A and ε>0. For a∈A, it is proved that the interior of the level set of (p,e−p)−ε pseudo spectrum of a is empty in the unbounded component of (p,e−p) resolvent set of a. An example is constructed to show that the condition ‘unbounded component’ can not be dropped. Further, it is proved this ‘unbounded component’ can be dropped in the case when A is B(X) where X is a complex uniformly convex Banach space. That is, if T∈B(X) then interior of the level set of (p,I−p)−ε pseudo spectrum is empty in (p,I−p) resolvent set of T.

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IITH Creators:
IITH CreatorsORCiD
D, SukumarUNSPECIFIED
Item Type: Article
Uncontrolled Keywords: Analytic vector valued map, (p,q)−ε pseudo spectrum, Complex uniformly convex Banach space
Subjects: Mathematics > Numerical analysis
Divisions: Department of Mathematics
Depositing User: Team Library
Date Deposited: 06 Jun 2017 10:28
Last Modified: 06 Jun 2017 10:30
URI: http://raiith.iith.ac.in/id/eprint/3193
Publisher URL: https://doi.org/10.1007/s41478-017-0039-4
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