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• W2000937796 abstract "Let f=(f1,…,fn) be an n-tuple of formal power series in noncommutative indeterminates Z1,…,Zn such that f(0)=0 and the Jacobian detJf(0)≠0, and let g=(g1,…,gn) be its inverse with respect to composition. We assume that f and g have nonzero radius of convergence and g is a bounded free holomorphic function on the open unit ball [B(H)n]1, where B(H) is the algebra of bounded linear operators an a Hilbert space H. In this paper, several results concerning the noncommutative multivariable operator theory on the unit ball [B(H)n]1− are extended to the noncommutative domainBf(H):={X∈B(H)n:g(f(X))=X and ‖f(X)‖⩽1} for an appropriate evaluation X↦f(X). We develop an operator model theory and dilation theory for Bf(H), where the associated universal model is an n-tuple (MZ1,…,MZn) of left multiplication operators acting on a Hilbert space H2(f) of formal power series. All the results of this paper have commutative versions." @default.
• W2000937796 created "2016-06-24" @default.
• W2000937796 creator A5007208241 @default.
• W2000937796 date "2012-04-01" @default.
• W2000937796 modified "2023-09-28" @default.
• W2000937796 title "Free biholomorphic functions and operator model theory" @default.
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• W2000937796 doi "https://doi.org/10.1016/j.jfa.2012.01.012" @default.
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