Convergence of Sequences of Linear Operators and Their Spectra

Boegli, Sabine

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
• Public URL: https://durham-repository.worktribe.com/output/1281120