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Zbl 1166.46029
Ergezen, Fuat
On unilateral weighted shifts in noncommutative operator theory. (English)
[J] Topology Appl. 155, No. 17-18, 1929-1934 (2008). ISSN 0166-8641

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.
[Mihai Putinar (Santa Barbara)]

MSC 2000:: *46H35 Topological algebras of operators
47A13 Several-variable spectral theory
47B37 Operators on sequence spaces, etc.
47L75 Other nonselfadjoint operator algebras

Keywords: weighted shift; Hardy space; rotationally symmetric measure; ball algebra

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