Remarks on the Convergence of Pseudospectra

Sabine Bögli*, Petr Siegl

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)
285 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)303-321
JournalIntegral Equations and Operator Theory
Issue number3
Early online date07 Sept 2014
Publication statusPublished - 01 Nov 2014


  • 47A10
  • 47A58

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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