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Pré-Publication, Document De Travail Année : 2015

A NONCOMMUTATIVE VERSION OF THE JULIA-WOLFF-CARATHEODORY THEOREM

Résumé

The classical Julia-Wolff-Carathéodory Theorem characterizes the behaviour of the derivative of an analytic self-map of a unit disc or of a half-plane of the complex plane at certain boundary points. We prove a version of this result that applies to noncommutative self-maps of noncommutative half-planes in von Neumann algebras at points of the distinguished boundary of the domain. Our result, somehow surprisingly, relies almost entirely on simple geometric properties of noncommutative half-planes, which are quite similar to the geometric properties of classical hyperbolic spaces.
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Dates et versions

hal-01217087 , version 1 (19-10-2015)
hal-01217087 , version 2 (29-12-2015)
hal-01217087 , version 3 (22-01-2016)

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Citer

Serban Belinschi. A NONCOMMUTATIVE VERSION OF THE JULIA-WOLFF-CARATHEODORY THEOREM. 2015. ⟨hal-01217087v1⟩
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