Abstract
A noncommutative domain Bφ(H)⊂B(H)n generated by the certain class of n-tuples φ=(φ1,⋯,φn) of formal power series in noncommutative indeterminates Z1,⋯,Zn, admits a universal model MZ=(MZ1,⋯, MZn), acting on a model space H2(φ). In this paper, we provide an explicit description of the wandering subspace W(Q)=Q⊖∑i=1n(MZi⊗IG)Q, where Q is an arbitrary joint invariant subspace under the operators MZ1⊗IG,⋯,MZn⊗IG. Moreover, we also provide a transfer function type characterization of the MZ-inner operators. This extends to the noncommutative setting the corresponding result obtained by Olofsson [7], [8] (when n=1) and by Eschmeier [3] in the multivariable commutative case.
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