Opuscula Math. 43, no. 1 (2023), 101-108

Opuscula Mathematica

A note on Hausdorff convergence of pseudospectra

Marko Lindner
Dennis Schmeckpeper

Abstract. For a bounded linear operator on a Banach space, we study approximation of the spectrum and pseudospectra in the Hausdorff distance. We give sufficient and necessary conditions in terms of pointwise convergence of appropriate spectral quantities.

Keywords: resolvent, spectrum, pseudospectrum, Hausdorff convergence.

Mathematics Subject Classification: 47A10, 47A25.

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  • Marko Lindner (corresponding author)
  • TU Hamburg, Institute of Mathematics, Am Schwarzenberg - Campus 1, 21073 Hamburg, Germany
  • Dennis Schmeckpeper
  • TU Hamburg, Institute of Mathematics, Am Schwarzenberg - Campus 1, 21073 Hamburg, Germany
  • Communicated by P.A. Cojuahri.
  • Received: 2022-10-13.
  • Revised: 2022-11-01.
  • Accepted: 2022-11-05.
  • Published online: 2022-12-30.
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Cite this article as:
Marko Lindner, Dennis Schmeckpeper, A note on Hausdorff convergence of pseudospectra, Opuscula Math. 43, no. 1 (2023), 101-108, https://doi.org/10.7494/OpMath.2023.43.1.101

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