Journal of Operator Theory

Volume 91, Issue 2, Spring 2024 pp. 399-419.

Commutant lifting in the Schur--Agler class

Authors: Sibaprasad Barik (1), Monojit Bhattacharjee (2), B. Krishna Das (3)
Author institution: (1) Department of Mathematics, Ben-Gurion University of the Negev, P.O.B. 653, Be'er Sheva 8410501, Israel
(2) Department of Mathematics, Birla Institute of Technology and Science -Pilani, K.K. Birla Goa Campus, Goa, 403726, India
(3) Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

Summary: In this article we study commutant lifting theorems, more generally intertwining lifting theorems, for weighted Bergman spaces over the unit ball in ${\mathbb C}^n$. In the particular case of the Hardy space over the unit disc and the Drury-Arveson space over the unit ball, our commutant lifting theorem provides an alternative proof of the classical commutant lifting theorems of Sarason and Ball, Trent and Vinnikov.

DOI: http://dx.doi.org/10.7900/jot.2022apr27.2372
Keywords: commutant lifting, intertwining lifting, Schur--Agler functions, hypercontractions, Drury-Arveson space, weighted Bergman spaces

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