1Katedra Zastosowa/n Matematyki Uniwersytet Rolniczy w Krakowie Al. Mickiewicza 24/28 30-059 Kraków, Poland 2Instytut Matematyki Uniwersytet Jagiello/nski ul. /Lojasiewicza 6 30-348 Kraków, Poland
Studia Mathematica, Tome 193 (2009) no. 1, pp. 29-52
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.
Keywords:
previous paper have characterized joint subnormality semigroup composition operators space positive definiteness radon nikodym derivatives attached each rational point present paper groups composition operators space positive definiteness requirement replaced kind consistency condition which seems simpler work turns out consistency condition characterizes subnormality semigroups composition operators space induced injective bimeasurable transformations consistency condition formulated language laplace transform takes multiplicative form paper concludes examples
Affiliations des auteurs :
Piotr Budzy/nski
1
;
Jan Stochel
2
1
Katedra Zastosowa/n Matematyki Uniwersytet Rolniczy w Krakowie Al. Mickiewicza 24/28 30-059 Kraków, Poland
2
Instytut Matematyki Uniwersytet Jagiello/nski ul. /Lojasiewicza 6 30-348 Kraków, Poland
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author = {Piotr Budzy/nski and Jan Stochel},
title = {Joint subnormality of $n$-tuples and
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journal = {Studia Mathematica},
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Piotr Budzy/nski; Jan Stochel. Joint subnormality of $n$-tuples and
$C_0$-semigroups of composition operators on $L^2$-spaces, II. Studia Mathematica, Tome 193 (2009) no. 1, pp. 29-52. doi: 10.4064/sm193-1-2
