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January 2019 Spectral picture for rationally multicyclic subnormal operators
Liming Yang
Banach J. Math. Anal. 13(1): 151-173 (January 2019). DOI: 10.1215/17358787-2018-0020

Abstract

For a pure bounded rationally cyclic subnormal operator S on a separable complex Hilbert space H , Conway and Elias showed that clos ( σ ( S ) σ e ( S ) ) = clos ( Int ( σ ( S ) ) ) . This article examines the property for rationally multicyclic ( N -cyclic) subnormal operators. We show that there exists a 2 -cyclic irreducible subnormal operator S with clos ( σ ( S ) σ e ( S ) ) clos ( Int ( σ ( S ) ) ) . We also show the following. For a pure rationally N -cyclic subnormal operator S on H with the minimal normal extension M on K H , let K m = clos ( span { ( M ) k x : x H , 0 k m } . Suppose that M | K N 1 is pure. Then clos ( σ ( S ) σ e ( S ) ) = clos ( Int ( σ ( S ) ) ) .

Citation

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Liming Yang. "Spectral picture for rationally multicyclic subnormal operators." Banach J. Math. Anal. 13 (1) 151 - 173, January 2019. https://doi.org/10.1215/17358787-2018-0020

Information

Received: 14 March 2018; Accepted: 21 June 2018; Published: January 2019
First available in Project Euclid: 28 September 2018

zbMATH: 07002036
MathSciNet: MR3894066
Digital Object Identifier: 10.1215/17358787-2018-0020

Subjects:
Primary: 47B20
Secondary: 30H99, 47A16

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 1 • January 2019
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