Convergence of Sequences of Linear Operators and Their Spectra

Boegli, Sabine

doi:10.1007/s00020-017-2389-3

Convergence of Sequences of Linear Operators and Their Spectra

Boegli, Sabine

Authors

Dr Sabine Boegli sabine.boegli@durham.ac.uk
Associate Professor

Abstract

We establish spectral convergence results of approximations of unbounded non-selfadjoint linear operators with compact resolvents by operators that converge in generalized strong resolvent sense. The aim is to establish general assumptions that ensure spectral exactness, i.e. that every true eigenvalue is approximated and no spurious eigenvalues occur. A main ingredient is the discrete compactness of the sequence of resolvents of the approximating operators. We establish sufficient conditions and perturbation results for strong convergence and for discrete compactness of the resolvents.

Citation

Boegli, S. (2017). Convergence of Sequences of Linear Operators and Their Spectra. Integral Equations and Operator Theory, 88(4), 559-599. https://doi.org/10.1007/s00020-017-2389-3

Journal Article Type	Article
Online Publication Date	Jul 24, 2017
Publication Date	Aug 31, 2017
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	88
Issue	4
Pages	559-599
DOI	https://doi.org/10.1007/s00020-017-2389-3

Files

Accepted Journal Article (451 Kb)
PDF

Copyright Statement
This is a post-peer-review, pre-copyedit version of an article published in Integral equations and operator theory. The final authenticated version is available online at: https://doi.org/10.1007/s00020-017-2389-3