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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Operator theory on noncommutative varieties, II

Author: Gelu Popescu
Journal: Proc. Amer. Math. Soc. 135 (2007), 2151-2164
MSC (2000): Primary 47A20, 47A56; Secondary 47A13, 47A63
Published electronically: March 1, 2007
MathSciNet review: 2299493
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Abstract: An $ n$-tuple of operators $ T:=[T_1,\ldots, T_n]$ on a Hilbert space $ \mathcal{H}$ is called a $ J$-constrained row contraction if $ T_1T_1^*+\cdots + T_nT_n^*\leq I_\mathcal{H}$ and

$\displaystyle f(T_1,\ldots, T_n)=0,\quad f\in J, $

where $ J$ is a WOT-closed two-sided ideal of the noncommutative analytic Toeplitz algebra $ F_n^\infty$ and $ f(T_1,\ldots, T_n)$ is defined using the $ F_n^\infty$-functional calculus for row contractions.

We show that the constrained characteristic function $ \Theta_{J,T}$ associated with $ J$ and $ T$ is a complete unitary invariant for $ J$-constrained completely non-coisometric (c.n.c.) row contractions. We also provide a model for this class of row contractions in terms of the constrained characteristic functions. In particular, we obtain a model theory for $ q$-commuting c.n.c. row contractions.

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Additional Information

Gelu Popescu
Affiliation: Department of Mathematics, The University of Texas at San Antonio, San Antonio, Texas 78249

Keywords: Multivariable operator theory, noncommutative variety, characteristic function, model theory, row contraction, constrained shift, Poisson kernel, Fock space, unitary invariant, von Neumann inequality
Received by editor(s): September 19, 2005
Received by editor(s) in revised form: March 20, 2006
Published electronically: March 1, 2007
Additional Notes: This research was supported in part by an NSF grant
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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