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Convergence of sequences of linear operators and their spectra.

Boegli, Sabine (2017) 'Convergence of sequences of linear operators and their spectra.', Integral equations and operator theory., 88 (4). pp. 559-599.


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.

Item Type:Article
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Publisher 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:
Date accepted:No date available
Date deposited:12 December 2019
Date of first online publication:24 July 2017
Date first made open access:12 December 2019

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