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Convergence of Sequences of Linear Operators and Their Spectra

Boegli, Sabine

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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

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