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Local convergence of spectra and pseudospectra

Boegli, Sabine

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Abstract

We prove local convergence results for the spectra and pseudospectra of sequences of linear operators acting in different Hilbert spaces and converging in generalised strong resolvent sense to an operator with possibly non-empty essential spectrum. We establish local spectral exactness outside the limiting essential spectrum, local ε-pseudospectral exactness outside the limiting essential ε-near spectrum, and discuss properties of these two notions including perturbation results.

Citation

Boegli, S. (2018). Local convergence of spectra and pseudospectra. Journal of Spectral Theory, 8(3), 1051-1098. https://doi.org/10.4171/jst/222

Journal Article Type Article
Online Publication Date Jul 15, 2018
Publication Date Jul 15, 2018
Deposit Date Dec 11, 2019
Publicly Available Date Dec 12, 2019
Journal Journal of Spectral Theory
Print ISSN 1664-039X
Electronic ISSN 1664-0403
Publisher EMS Press
Peer Reviewed Peer Reviewed
Volume 8
Issue 3
Pages 1051-1098
DOI https://doi.org/10.4171/jst/222
Public URL https://durham-repository.worktribe.com/output/1281628

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