Unitary equivalence of operator-valued multishifts

Rajeev Gupta; Surjit Kumar; Shailesh Trivedi

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arXiv · 1904.00983

Unitary equivalence of operator-valued multishifts

Rajeev Gupta·Surjit Kumar·Shailesh Trivedi

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Abstract

We systematically study various aspects of operator-valued multishifts. Beginning with basic properties, we show that the class of multishifts on the directed Cartesian product of rooted directed trees is contained in that of operator-valued multishifts. Further, we establish circularity, analyticity and wandering subspace property of these multishifts. In the rest part of the paper, we study the function theoretic behaviour of operator-valued multishifts. We determine the bounded point evaluation, reproducing kernel structure and the unitary equivalence of operator-valued multishifts with invertible operator weights. In contrast with a result of Lubin, it appears that the set of all bounded point evaluations of an operator-valued multishift may be properly contained in the joint point spectrum of the adjoint of underlying multishift.

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BibTeX RIS

Rajeev Gupta, Surjit Kumar, Shailesh Trivedi. 2019-04-01. Unitary equivalence of operator-valued multishifts. https://arxiv.org/abs/1904.00983

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