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arXiv · 2401.12144

A short note on similarity of operator-valued multishifts

Soumitra Ghara·Surjit Kumar·Shailesh Trivedi
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Abstract

A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary equivalence of two (multi)shifts. Further, we utilize the aforementioned similarity criteria to determine the similarity between two tuples of operators of multiplication by the coordinate functions on certain reproducing kernel Hilbert spaces determined by diagonal kernels.

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Soumitra Ghara, Surjit Kumar, Shailesh Trivedi. 2024-01-22. A short note on similarity of operator-valued multishifts. https://arxiv.org/abs/2401.12144

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