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arXiv · 2508.00763

Unitary equivalence of balanced weighted shifts on rooted directed trees

Shubhankar Mandal·Shailesh Trivedi
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Abstract

We completely characterize non-periodic balanced weighted shifts $S_{\lambdab}$ on rooted directed trees under a very mild assumption that $S_{\lambdab}^{*n}S_{\lambdab}^n|_{\ker S_{\lambdab}^*}$ is invertible operator on $\ker S_{\lambdab}^*$ for all $n \in \mathbb N$. This generalizes the previously established unitary equivalences for Bergman and Dirichlet type shifts associated with locally finite rooted directed trees. We also give a counter example to justify that the criteria obtained for non-periodic balanced weighted shifts is not necessary for eventually periodic balanced weighted shifts.

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Shubhankar Mandal, Shailesh Trivedi. 2025-08-01. Unitary equivalence of balanced weighted shifts on rooted directed trees. https://arxiv.org/abs/2508.00763

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