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Unitary equivalence of operator-valued multishifts

Gupta, R and Kumar, S and Trivedi, S (2020) Unitary equivalence of operator-valued multishifts. In: Journal of Mathematical Analysis and Applications, 487 (2).

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Official URL: https://dx.doi.org/10.1016/j.jmaa.2020.124032


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.

Item Type: Journal Article
Publication: Journal of Mathematical Analysis and Applications
Publisher: Academic Press Inc.
Additional Information: The copyright of this article belongs to Academic Press Inc.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 17 Jun 2020 09:56
Last Modified: 17 Jun 2020 09:56
URI: http://eprints.iisc.ac.in/id/eprint/64942

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