Linear resolvent growth of rank one perturbation of a unitary operator does not imply its similarity to a normal operator.

DOI10.1007/BF02868483zbMath1041.47007OpenAlexW1981876925MaRDI QIDQ1809921

Nikolai Nikolski, S. R. Treil'

Publication date: 2002

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02868483

zbMATH Keywords

resolventperturbationsimilaritynormal operator

Mathematics Subject Classification ID

Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Spectrum, resolvent (47A10) Perturbation theory of linear operators (47A55)

Related Items (10)

Completeness and spectral synthesis of nonselfadjoint one-dimensional perturbations of selfadjoint operators ⋮ The Two Weight Inequality for the Hilbert Transform: A Primer ⋮ Singular Integrals, Rank One Perturbations and Clark Model in General Situation ⋮ A two weight inequality for the Hilbert transform assuming an energy hypothesis ⋮ A Good-λ Lemma, Two Weight T1 Theorems Without Weak Boundedness, and a Two Weight Accretive Global Tb Theorem ⋮ The two weight \(T1\) theorem for fractional Riesz transforms when one measure is supported on a curve ⋮ Two-weight inequality for the Hilbert transform: a real variable characterization. I ⋮ Resolvent criteria for similarity to a normal operator with spectrum on a curve ⋮ The Bellman function, the two-weight Hilbert transform, and embeddings of the model spaces \(K_\theta\) ⋮ Recent developments in two weight testing theory

Cites Work

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• On the existence of a largest subharmonic minorant of a given function
• Conditions for similarity to unitary and self-adjoint operators
• A function model and some problems in the spectral theory of functions
• Linear resolvent growth test for similarity of a weak contraction to a normal operator
• Commuting spectral measures on Hilbert space
• Resolvent Tests for Similarity to a Normal Operator
• Linear resolvent growth of a weak contraction does not imply its similarity to a normal operator

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