Journal of Operator Theory

Volume 85, Issue 2, Spring 2021 pp. 443-462.

Factors of hypercontractions

Authors: Monojit Bhattacharjee (1), B. Krishna Das (2)
Author institution:(1) Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India
(2) Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

Summary: In this article, we study a class of contractive factors of $m$-hypercontractions for $m\in \mathbb{N}$. We find a characterization of such factors and it is achieved by finding explicit dilations of these factors on certain weighted Bergman spaces. This is a generalization of the work done by B.K. Das, S. Sarkar, J. Sarkar, Factorization of contraction, $\textit{Adv. in Math. } \textbf{322}(2017), 186-200$.

DOI: http://dx.doi.org/10.7900/jot.2019nov02.2273
Keywords: hypercontraction, Bergman space over the unit disc, commuting contractions, bounded analytic functions

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