Local convergence of spectra and pseudospectra

Boegli, Sabine

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
• Publisher: EMS Press
• Peer Reviewed: Peer Reviewed
• Volume: 8
• Issue: 3
• Pages: 1051-1098
• DOI: https://doi.org/10.4171/jst/222