Free biholomorphic classification of noncommutative domains

Abstract

In this paper we develop a theory of free holomorphic functions on noncommutative Reinhardt domains generated by positive regular free holomorphic functions in n noncommuting variables. We show that the free biholomorphic classification of these domains is the same as the classification, up to unital completely isometric isomorphisms, of the corresponding noncommutative domain algebras.

40 pages, corrected typos

References in corpus (2)

• Noncommutative ball maps
• Free Analysis Questions II: The Grassmannian Completion and The Series Expansions at the Origin