Quasinormal extensions of subnormal operator-weighted composition operators in ℓ2-spaces

We prove the subnormality of an operator-weighted composition operator whose symbol is a transformation of a discrete measure space and whose weights are multiplication operators in L2-spaces, under the assumption of existence of a family of probability measures whose Radon–Nikodym derivatives behav...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2017-08, Vol.452 (1), p.27-46
Main Authors: Budzyński, Piotr, Dymek, Piotr, Płaneta, Artur
Format: Article
Language:English
Subjects:
Operator-weighted composition operator
Quasinormal operator
Subnormal operator
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Summary:We prove the subnormality of an operator-weighted composition operator whose symbol is a transformation of a discrete measure space and whose weights are multiplication operators in L2-spaces, under the assumption of existence of a family of probability measures whose Radon–Nikodym derivatives behave regular along the trajectories of the symbol. We build the quasinormal extension, which is a weighted composition operator induced by the same symbol. We give auxiliary results concerning commutativity of operator-weighted composition operators with multiplication operators.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.02.057