Banach Journal of Mathematical Analysis

Spectral picture for rationally multicyclic subnormal operators

Liming Yang

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For a pure bounded rationally cyclic subnormal operator S on a separable complex Hilbert space H, Conway and Elias showed that clos(σ(S)σe(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)σe(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 KH, let Km=clos(span{(M)kx:xH,0km}. Suppose that M|KN1 is pure. Then clos(σ(S)σe(S))=clos(Int(σ(S))).

Article information

Banach J. Math. Anal., Volume 13, Number 1 (2019), 151-173.

Received: 14 March 2018
Accepted: 21 June 2018
First available in Project Euclid: 28 September 2018

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Zentralblatt MATH identifier

Primary: 47B20: Subnormal operators, hyponormal operators, etc.
Secondary: 47A16: Cyclic vectors, hypercyclic and chaotic operators 30H99: None of the above, but in this section

spectral picture multicyclic subnormal operators


Yang, Liming. Spectral picture for rationally multicyclic subnormal operators. Banach J. Math. Anal. 13 (2019), no. 1, 151--173. doi:10.1215/17358787-2018-0020.

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