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arXiv · 1806.03229

Complete systems of unitary invariants for some classes of $2$-isometries

Akash Anand·Sameer Chavan·Zenon Jan Jabłoński·Jan Stochel
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Abstract

The unitary equivalence of $2$-isometric operators satisfying the so-called kernel condition is characterized. It 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. A complete system of unitary invariants for $2$-isometric weighted shifts on rooted directed trees satisfying the kernel condition is provided. It is formulated purely in the langauge of graph-theory, namely in terms of certain generation branching degrees. The membership of the Cauchy dual operators of $2$-isometries in classes $C_{0 \cdot}$ and $C_{\cdot 0}$ is also studied.

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Akash Anand, Sameer Chavan, Zenon Jan Jabłoński, Jan Stochel. 2018-06-08. Complete systems of unitary invariants for some classes of $2$-isometries. https://arxiv.org/abs/1806.03229

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