Abstract
The Sz.-Nagy-FoiaŞ functional model for completely non-unitary contractions is extended to completely non-coisometric sequences of bounded operatorsT = (T1,...,T d) (d finite or infinite) on a Hilbert space, with bounded characteristic functions. For this class of sequences, it is shown that the characteristic function θT is a complete unitary invariant.
We obtain, as the main result, necessary and sufficient conditions for a bounded multi-analytic operator on Fock spaces to coincide with the characteristic function associated with a completely non-coisometric sequence of bounded operators on a Hilbert space.
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Research supported in part by a COBASE grant from the National Research Council.
The first author was partially supported by a grant from Ministerul Educaţiei Şi Cercetarii.
The second author was partially supported by a National Science Foundation grant.
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Gheondea, A., Popescu, G. Bounded characteristic functions and models for noncontractive sequences of operators. Integr equ oper theory 45, 15–38 (2003). https://doi.org/10.1007/BF02789592
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DOI: https://doi.org/10.1007/BF02789592