Free biholomorphic functions and operator model theory,II

TL;DR

This paper extends free biholomorphic function theory and operator models from the unit ball to other noncommutative domains and varieties, focusing on the non-coisometric and variety cases.

Contribution

It advances the transfer of free Nagy-Foias theory to broader noncommutative settings, including non-coisometric operators and varieties.

Findings

Develops operator models for non-coisometric cases

Extends theory to noncommutative varieties

Provides new tools for noncommutative function theory

Abstract

This is a continuation of the paper entitled "Free biholomorphic functions and operator model theory", in our attempt to transfer the free analogue of Nagy-Foias theory from the unit ball $[B(\cH)^n]_1$ to other noncommutative domains and varieties in $B(\cH)^n$, using appropriate maps. The present paper treats the completely non-coisometric case and the case of noncommutative varieties.