Remarks on the Convergence of Pseudospectra

Boegli, Sabine; Siegl, Petr

doi:10.1007/s00020-014-2178-1

Remarks on the Convergence of Pseudospectra

Boegli, Sabine; Siegl, Petr

Authors

Dr Sabine Boegli sabine.boegli@durham.ac.uk
Associate Professor

Petr Siegl

Abstract

We establish the convergence of pseudospectra in Hausdorff distance for closed operators acting in different Hilbert spaces and converging in the generalised norm resolvent sense. As an assumption, we exclude the case that the limiting operator has constant resolvent norm on an open set. We extend the class of operators for which it is known that the latter cannot happen by showing that if the resolvent norm is constant on an open set, then this constant is the global minimum. We present a number of examples exhibiting various resolvent norm behaviours and illustrating the applicability of this characterisation compared to known results.

Citation

Boegli, S., & Siegl, P. (2014). Remarks on the Convergence of Pseudospectra. Integral Equations and Operator Theory, 80(3), 303-321. https://doi.org/10.1007/s00020-014-2178-1

Journal Article Type	Article
Online Publication Date	Sep 7, 2014
Publication Date	Nov 30, 2014
Deposit Date	Dec 11, 2019
Publicly Available Date	Dec 12, 2019
Journal	Integral Equations and Operator Theory
Print ISSN	0378-620X
Electronic ISSN	1420-8989
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	80
Issue	3
Pages	303-321
DOI	https://doi.org/10.1007/s00020-014-2178-1

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Copyright Statement
This is a post-peer-review, pre-copyedit version of an article published in Integral equations and operator theory. The final authenticated version is available online at: https://doi.org/10.1007/s00020-014-2178-1