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On unilateral weighted shifts in noncommutative operator theory. (English) Zbl 1166.46029
The author studies the $n$-tuple $M_z$ of multiplication operators by the complex variables $z_1,\dots,z_n$ on the closure of polynomials in $\Bbb C^n$ with respect to a rotationally symmetric, positive measure supported by the unit ball. The interplay between a weighted shift representation of these operators and the functional model leads to a characterization of the operator algebra generated by $M_z$. In the background of the proof lie a multivariate moment problem and von Neumann type inequalities.

##### MSC:
 46H35 Topological algebras of operators 47A13 Several-variable spectral theory 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 47L75 Other nonselfadjoint operator algebras
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##### References:
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