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arXiv · 1606.02476

Quasinormal extensions of subnormal operator-weighted composition operators in $\ell^2$-spaces

Piotr Budzynski·Piotr Dymek·Artur Planeta
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Abstract

We prove the subnormality of an operator-weighted composition operator whose symbol is a transformation of a discrete measure space and weights are multiplication operators in $L^2$-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.

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Piotr Budzynski, Piotr Dymek, Artur Planeta. 2016-06-08. Quasinormal extensions of subnormal operator-weighted composition operators in $\ell^2$-spaces. https://doi.org/10.1016/j.jmaa.2017.02057

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