Journal of Operator Theory

Volume 88, Issue 2, Fall 2022 pp. 479-510.

Hypercontractions and factorizations of multipliers in one and several variables

Authors: Monojit Bhattacharjee (1), B. Krishna Das (2), Jaydeb Sarkar (3)
Author institution:(1) Department of Mathematics, Birla Institute of Technology and Science -Pilani, K.K. Birla Goa Campus, Goa, 403726, India
(2) Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India
(3) Indian Statistical Institute, Statistics and Mathematics Unit, 8th Mile, Mysore Road, Bangalore, 560059, India

Summary: 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 Foias characteristic functions of contractions. We pre\-sent 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 $\mathbb{C}^n$. 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.

DOI: http://dx.doi.org/10.7900/jot.2021apr01.2362
Keywords: hypercontractions, weighted Bergman spaces, Bergman inner functions, analytic models, characteristic functions, factorizations of multipliers, joint invariant subspaces

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