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Resolvent criteria for similarity to a normal operator with spectrum on a curve

Lookup NU author(s): Dr Michael DritschelORCiD, Daniel Estevez Sanchez

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Abstract

© 2018 Elsevier Inc. We give some new criteria for a Hilbert space operator with spectrum on a smooth curve to be similar to a normal operator, in terms of pointwise and integral estimates of the resolvent. These results generalize criteria of Stampfli, Van Casteren and Naboko, and answers several questions posed by Stampfli in [48]. The main tools are from our recent results [12] on dilation to the boundary of the spectrum, along with the Dynkin functional calculus for smooth functions, which is based on pseudoanalytic continuation.

Publication metadata

Author(s): Dritschel MA, Estevez D, Yakubovich D

Publication type: Article

Publication status: Published

Journal: Journal of Mathematical Analysis and Applications

Year: 2018

Volume: 463

Issue: 1

Pages: 345-364

Print publication date: 01/07/2018

Online publication date: 16/04/2018

Acceptance date: 13/07/2017

ISSN (print): 0022-247X

ISSN (electronic): 1096-0813

Publisher: Academic Press Inc.

URL: https://doi.org/10.1016/j.jmaa.2018.03.026

DOI: 10.1016/j.jmaa.2018.03.026

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