Remarks on the convergence of pseudospectra

Bögli, Sabine; Siegl, Petr (2014). Remarks on the convergence of pseudospectra. Integral equations and operator theory, 80(3), pp. 303-321. Birkhäuser 10.1007/s00020-014-2178-1

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Bögli, Sabine and Siegl, Petr

Subjects:

500 Science > 510 Mathematics

ISSN:

0378-620X

Publisher:

Birkhäuser

Language:

English

Submitter:

Mario Amrein

Date Deposited:

14 Apr 2015 15:45

Last Modified:

07 Oct 2015 10:25

Publisher DOI:

10.1007/s00020-014-2178-1

BORIS DOI:

10.7892/boris.66711

URI:

https://boris.unibe.ch/id/eprint/66711

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