Quasinormal extensions of subnormal operator-weighted composition operators in $\ell^2$-spaces
Functional Analysis
2018-09-06 v1
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 -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.
Cite
@article{arxiv.1606.02476,
title = {Quasinormal extensions of subnormal operator-weighted composition operators in $\ell^2$-spaces},
author = {Piotr Budzynski and Piotr Dymek and Artur Planeta},
journal= {arXiv preprint arXiv:1606.02476},
year = {2018}
}