Journal of Operator Theory

Volume 47, Issue 2, Spring 2002 pp. 287-302.

Operator tuples and analytic models over general domains in $\C^{n}$

Authors: C. Ambrozie (1), M. Englis (2), and V. Muller (3)
Author institution: (1) Institute of Mathematics of the Romanian Academy, P.O. Box 1--764, 70700 Bucharest, Romania
(2) Mathematical Institute, Academy of Sciences of the Czech Republic, 115 67 Prague 1, Zitna 25, Czech Republic
(3) Mathematical Institute, Academy of Sciences of the Czech Republic, 115 67 Prague 1, Zitna 25, Czech Republic

Summary: For a class of Hilbert spaces ${\H}$ of functions analytic on a domain $D\subset \C^n$, we characterize the $n$-tuples $T$ of commuting Hilbert space operators which can be represented by means of multiplications by the coordinate functions on ${\H}$. In~case $\H$ is a subspace of some $L^2$-space we thus obtain for such $T$ a normal dilation constructed in terms of the reproducing kernel of ${\H}$. This generalizes known results of this type and provides new models in a large class of functional Hilbert spaces, including the standard weighted Bergman spaces of analytic functions on bounded symmetric domains.

Keywords: Joint dilation, reproducing kernel

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