Weighted shifts and commuting normal extension

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Abstract
The main result of this paper shows that the existence of commuting normal extension (c.n.e.) for an arbitrary family of commuting subnormal operators can be determined by considering appropriate families of multivariable weighted shifts. In proving this some known criteria for c.n.e. are generalized. It is also shown that a family of jointly quasi-normal operators has c.n.e.

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