Skip to main content

Research Repository

Advanced Search

Remarks on the Convergence of Pseudospectra

Boegli, Sabine; Siegl, Petr

Remarks on the Convergence of Pseudospectra Thumbnail


Petr Siegl


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.


Boegli, S., & Siegl, P. (2014). Remarks on the Convergence of Pseudospectra. Integral Equations and Operator Theory, 80(3), 303-321.

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


You might also like

Downloadable Citations