Noncommutative hyperbolic metrics

Abstract

We characterize certain noncommutative domains in terms of noncommutative holomorphic equivalence via a pseudometric that we define in purely algebraic terms. We prove some properties of this pseudometric and provide an application to free probability.

Second version: expanded introduction, several modifications, including the definition of a new distance, a correction in Proposition 4.7, and a strengthening of the free probability results. Comments welcome

References in corpus (4)

• Proper Analytic Free Maps
• Representation of free Herglotz functions
• Global holomorphic functions in several non-commuting variables II
• On fixed points of self maps of the free ball

Cited by in corpus (2)

• Algebras of noncommutative functions on subvarieties of the noncommutative ball: the bounded and completely bounded isomorphism problem
• The atoms of the free additive convolution of two operator-valued distributions