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

D, Sukumar and Veeramani, S (2020) Level sets of (p,e-p)outer generalized pseudo spectrum. Journal of Analysis, 28 (1). 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 Creators	ORCiD
D, Sukumar	https://orcid.org/0000-0002-3112-6752

Item Type:

Article

Additional Information:

The authors are thankful to the anonymous referee for the valuable suggestions towards the improvement of this paper. Research of the first author was supported by the Department of Science and Technology (DST), India (No: SB/FTP/MS-015/2013). Second author thanks the University Grants Commission (UGC), India for the financial support provided as a form of Research Fellowship to carry out this research work at IIT Hyderabad.

Uncontrolled Keywords:

Analytic vector valued map, (p,q)−ε pseudo spectrum, Complex uniformly convex Banach space

Subjects:

Mathematics

Divisions:

Department of Mathematics

Depositing User:

Team Library

Date Deposited:

06 Jun 2017 10:28

Last Modified:

24 Nov 2022 11:30