HYPERCONTRACTIONS AND FACTORIZATIONS OF MULTIPLIERS IN ONE AND SEVERAL VARIABLES

Article Type

Research Article

Publication Title

Journal of Operator Theory

Abstract

We introduce the notion of characteristic functions for commuting tuples of hypercontractions on Hilbert spaces, as a generalization of the notion of Sz.-Nagy and Foiaş characteristic functions of contractions. We present an explicit method to compute characteristic functions of hypercontractions and relate characteristic functions by means of the factors of Schur–Agler class of functions and universal multipliers on the unit ball in Cn. We also offer some factorization properties of multipliers. Characteristic functions of hypercontrations are a complete unitary invariant. The Drury–Arveson space and the weighted Bergman spaces on the unit ball continue to play a significant role in our consideration. Our results are new even in the special case of single hypercontractions.

First Page

479

Last Page

510

DOI

10.7900/jot.2021apr01.2362

Publication Date

1-1-2022

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