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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.

46H35Topological algebras of operators
47A13Several-variable spectral theory
47B37Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47L75Other nonselfadjoint operator algebras
Full Text: DOI
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[2] Loginov, A. I.; Sulman, V. S.: Invariant subspace of operator algebras. Mathematical analysis, itogi nauki i tekniki akad. Nauk. SSSR vsesojuz. Inst. naucn. Teh. informacaii 26, 65-145 (1981)
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[9] Rudin, W.: Function theory in the unit ball of cn. (1980) · Zbl 0495.32001