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arXiv · 2402.08770

Unitarily equivalent bilateral weighted shifts with operator weights

Michał Buchała
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Abstract

We study unitarily equivalent bilateral weighted shifts with operator weights. We establish a general characterization of unitary equivalence of such shifts under the assumption that the weights are quasi-invertible. We prove that under certain assumptions unitary equivalence of bilateral weighted shifts with operator weights defined on $ \mathbb{C}^{2} $ can always be given by a unitary operator with at most two non-zero diagonals. We provide examples of unitarily equivalent shifts with weights defined on $ \mathbb{C}^{k} $ such that every unitary operator, which intertwines them has at least $ k $ non-zero diagonals.

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Michał Buchała. 2024-02-13. Unitarily equivalent bilateral weighted shifts with operator weights. https://doi.org/10.7494/opmath.2024.44.5.651

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