Unitary equivalence of operator-valued multishifts

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:487

Article

Gupta, Rajeev¹  Kumar, Surjit²  Trivedi, Shailesh¹ 

[1] Indian Inst Technol Kanpur, Dept Math & Stat, Kanpur, Uttar Pradesh, India

[2] Indian Inst Sci Bangalore, Dept Math, Bangalore, Karnataka, India

关键词: Operator-valued multishift;    Circularity;    Operator-valued reproducing kernel;    Bounded point evaluation;    Wandering subspace property;   

DOI  :  10.1016/j.jmaa.2020.124032

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free