Free biholomorphic classification of noncommutative domains

Details Free biholomorphic classification of noncommutative domains Free biholomorphic classification of noncommutative domains

2010-03-26

arxiv.org/abs/1003.5139v2

Int.Math.Res.Not. 2011, no.4, 784-850

Mathematics

Operator Algebras

40 pages, corrected typos

Scientific paper

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.

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