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April 2019 Complete systems of unitary invariants for some classes of 2-isometries
Akash Anand, Sameer Chavan, Zenon Jan Jabłoński, Jan Stochel
Banach J. Math. Anal. 13(2): 359-385 (April 2019). DOI: 10.1215/17358787-2018-0042

Abstract

We characterize the unitary equivalence of 2-isometric operators satisfying the so-called kernel condition. This relies on a model for such operators built on operator-valued unilateral weighted shifts and on a characterization of the unitary equivalence of operator-valued unilateral weighted shifts in a fairly general context. We also provide a complete system of unitary invariants for 2-isometric weighted shifts on rooted directed trees satisfying the kernel condition. This is formulated purely in the language of graph theory—namely, in terms of certain generation branching degrees. Finally, we study the membership of the Cauchy dual operators of 2-isometries in classes C0 and C0.

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Akash Anand. Sameer Chavan. Zenon Jan Jabłoński. Jan Stochel. "Complete systems of unitary invariants for some classes of 2-isometries." Banach J. Math. Anal. 13 (2) 359 - 385, April 2019. https://doi.org/10.1215/17358787-2018-0042

Information

Received: 21 August 2018; Accepted: 29 November 2018; Published: April 2019
First available in Project Euclid: 1 February 2019

zbMATH: 07045463
MathSciNet: MR3927878
Digital Object Identifier: 10.1215/17358787-2018-0042

Subjects:
Primary: 47B20
Secondary: 47B37 , 47B49

Keywords: $C_{0\cdot }$ and $C_{\cdot 0}$ classes , 2-isometry , Cauchy dual operator , complete system of unitary invariants , kernel condition , weighted shift on a directed tree

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 2 • April 2019
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