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July 2019 Kernels of Hankel operators on the Hardy space over the bidisk
Kei Ji Izuchi, Kou Hei Izuchi, Yuko Izuchi
Banach J. Math. Anal. 13(3): 612-626 (July 2019). DOI: 10.1215/17358787-2019-0020

Abstract

For a Hankel operator Hξ, ξL(T2), on the Hardy space H2 over the bidisk, kerHξ¯ is an invariant subspace of H2. It is known that there is an invariant subspace M such that kerHξ¯M for every ξL. Let ηH be a nonconstant function. It is proved that if ηφ(z)H2+ψ(w)H2 for Blaschke products φ(z) and ψ(w), then kerHη¯=θ1(z)θ2(w)H2 for some subproducts θ1(z) and θ2(w) of φ(z) and ψ(w), respectively. If η is -cyclic, then it is easy to see that kerHη¯={0}. We give some examples η satisfying kerHη¯={0} but η is not -cyclic.

Citation

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Kei Ji Izuchi. Kou Hei Izuchi. Yuko Izuchi. "Kernels of Hankel operators on the Hardy space over the bidisk." Banach J. Math. Anal. 13 (3) 612 - 626, July 2019. https://doi.org/10.1215/17358787-2019-0020

Information

Received: 7 July 2018; Accepted: 2 April 2019; Published: July 2019
First available in Project Euclid: 20 June 2019

zbMATH: 07083764
MathSciNet: MR3978940
Digital Object Identifier: 10.1215/17358787-2019-0020

Subjects:
Primary: 47A15
Secondary: 32A35‎ , 47B35

Keywords: Blaschke product , Hanker operator , Hardy space over the bidisk , invariant subspace , ‎kernel‎

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 3 • July 2019
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