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November 2018 On pseudospectral radii of operators on Hilbert spaces
Boting Jia, Youling Feng
Ann. Funct. Anal. 9(4): 474-484 (November 2018). DOI: 10.1215/20088752-2017-0062

Abstract

For ε>0 and a bounded linear operator T acting on some Hilbert space, the ε-pseudospectrum of T is σε(T)={zC:(zIT)1>1/ε} and the ε-pseudospectral radius of T is rε(T)=sup {|z|:zσε(T)}. In this article, we provide a characterization of those operators T satisfying rε(T)=r(T)+ε for all ε>0. Here r(T) denotes the spectral radius of T.

Citation

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Boting Jia. Youling Feng. "On pseudospectral radii of operators on Hilbert spaces." Ann. Funct. Anal. 9 (4) 474 - 484, November 2018. https://doi.org/10.1215/20088752-2017-0062

Information

Received: 29 May 2017; Accepted: 18 October 2017; Published: November 2018
First available in Project Euclid: 25 May 2018

zbMATH: 07002085
MathSciNet: MR3871908
Digital Object Identifier: 10.1215/20088752-2017-0062

Subjects:
Primary: 47A10
Secondary: 47B20

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.9 • No. 4 • November 2018
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