Joint subnormality of $n$-tuples and $C_0$-semigroups of composition operators on $L^2$-spaces
Volume 179 / 2007
Studia Mathematica 179 (2007), 167-184 MSC: Primary 47B20, 47B33; Secondary 47D03, 20M20. DOI: 10.4064/sm179-2-4
Joint subnormality of a family of composition operators on $L^2$-space is characterized by means of positive definiteness of appropriate Radon–Nikodym derivatives. Next, simplified positive definiteness conditions guaranteeing joint subnormality of a $C_0$-semigroup of composition operators are supplied. Finally, the Radon–Nikodym derivatives associated to a jointly subnormal $C_0$-semigroup of composition operators are shown to be the Laplace transforms of probability measures (modulo a $C_0$-group of scalars) constituting a measurable family.