Quasinormal extensions of subnormal operator-weighted composition operators in ? 2-spaces

摘要

Abstract 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 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. ]]>