Abstract
In a companion to this paper, we introduced the class of n-tuples f=(f1,…,fn) of formal power series in noncommutative indeterminates Z1,…,Zn with the model property and developed an operator model theory for pure n-tuples of operators in noncommutative domains Bf(H)⊂B(H)n, where the associated universal model is an n-tuple (MZ1,…,MZn) of multiplication operators on a Hilbert space H2(f) of formal power series. In the present paper, we continue this work by considering the completely non-coisometric (c.n.c) case. In the second part of the paper, several results concerning the noncommutative multivariable operator theory on the unit ball [B(H)n]1− are extended to noncommutative varieties Vf,J(H)⊆Bf(H) defined byVf,J(H):={(T1,…,Tn)∈Bf(H):ψ(T1,…,Tn)=0 for any ψ∈J} for an appropriate evaluation ψ(T1,…,Tn) and associated with WOT-closed two-sided ideals J of the Hardy algebra H∞(Bf). In particular, we obtain commutative versions for all the results.
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