Quantitative spectral perturbation theory for compact operators on a Hilbert space
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Publication:6341600
DOI10.1016/J.LAA.2020.08.033arXiv2005.13891MaRDI QIDQ6341600
O. F. Bandtlow, Ayşe Güven Sarıhan
Publication date: 28 May 2020
Abstract: We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging to a particular compactness class. As a consequence we obtain explicitly computable upper bounds for the Hausdorff distance of the spectra of two operators belonging to the same compactness class in terms of the distance of the two operators in operator norm.
Linear operators defined by compactness properties (47B07) Spectrum, resolvent (47A10) Perturbation theory of linear operators (47A55)
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