Berezin transforms on noncommutative polydomains

TL;DR

This paper extends multivariable operator theory to noncommutative polydomains using Berezin transforms, unifying previous models for ball-like domains and polydiscs.

Contribution

It introduces a generalized framework for noncommutative polydomains and develops associated Berezin transforms, bridging commutative and noncommutative multivariable operator theories.

Findings

Unified operator model theory for noncommutative polydomains

Extension of Berezin transforms to new classes of domains

Connections established between commutative and noncommutative cases

Abstract

This paper is an attempt to unify the multivariable operator model theory for ball-like domains and commutative polydiscs, and extend it to a more general class of noncommutative polydomains. An important role in our study is played by noncommutative Berezin transforms associated with the elements of the polydomain.