Unitary equivalence of balanced weighted shifts on rooted directed trees

2025/08/01 by Mandal, Shubhankar, Trivedi, Shailesh
#05C20 #47B37 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2508.00763

Abstract

We completely characterize non-periodic balanced weighted shifts S_\lambdab on rooted directed trees under a very mild assumption that S_\lambdab^*nS_\lambdabⁿ|_ker S_\lambdab^* is invertible operator on ker S_\lambdab^* for all n ∈ \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.

Citations

• Unitary equivalence of operator-valued multishifts
• Analytic m-isometries without the wandering subspace property
• Complete systems of unitary invariants for some classes of 2-isometries
• Von Neumann's inequality for commuting operator-valued multishifts
• Dirichlet Spaces Associated With Locally Finite Rooted Directed Trees
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• Weighted shifts on directed trees. Their multiplier algebras, reflexivity and decompositions
• Multishifts on Directed Cartesian Product of Rooted Directed Trees
• Subnormality of unbounded composition operators over one-circuit\n directed graphs: exotic examples

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