Joint subnormality of $n$-tuples and $C_0$-semigroups of composition operators on $L^2$-spaces, II

Volume 193 / 2009

Piotr Budzy/nski, Jan Stochel Studia Mathematica 193 (2009), 29-52 MSC: Primary 47B20, 47B33; Secondary 47D03, 20M20. DOI: 10.4064/sm193-1-2


In the previous paper, we have characterized (joint) subnormality of a $C_0$-semigroup of composition operators on $L^2$-space by positive definiteness of the Radon–Nikodym derivatives attached to it at each rational point. In the present paper, we show that in the case of $C_0$-groups of composition operators on $L^2$-space the positive definiteness requirement can be replaced by a kind of consistency condition which seems to be simpler to work with. It turns out that the consistency condition also characterizes subnormality of $C_0$-semigroups of composition operators on $L^2$-space induced by injective and bimeasurable transformations. The consistency condition, when formulated in the language of the Laplace transform, takes a multiplicative form. The paper concludes with some examples.


  • Piotr Budzy/nskiKatedra Zastosowa/n Matematyki
    Uniwersytet Rolniczy w Krakowie
    Al. Mickiewicza 24/28
    30-059 Kraków, Poland
  • Jan StochelInstytut Matematyki
    Uniwersytet Jagiello/nski
    ul. /Lojasiewicza 6
    30-348 Kraków, Poland

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