Quantitative spectral perturbation theory for compact operators on a\n Hilbert space

2020/05/28 by Ayşe Güven, Guven, Ayse, Oscar F. Bandtlow +2 · 1 citation
Computer Science · Mathematics · #47A55 (Primary) 7A10 #47B07 (Secondary) #Advanced Banach Space Theory #Advanced Mathematical Modeling in Engineering #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2005.13891

openalex publication_date 2020/05/28 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We introduce compactness classes of Hilbert space operators by grouping\ntogether all operators for which the associated singular values decay at a\ncertain speed and establish upper bounds for the norm of the resolvent of\noperators belonging to a particular compactness class. As a consequence we\nobtain explicitly computable upper bounds for the Hausdorff distance of the\nspectra of two operators belonging to the same compactness class in terms of\nthe distance of the two operators in operator norm.\n

Citations

• Norms and exclusion theorems

Cited by

• A pseudospectral approach to rigorous numerical estimation of Ruelle resonances of transfer operators

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