Joint subnormality of $n$-tuples and
$C_0$-semigroups of composition operators on $L^2$-spaces
Studia Mathematica, Tome 179 (2007) no. 2, pp. 167-184
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
joint subnormality family composition operators space characterized means positive definiteness appropriate radon nikodym derivatives simplified positive definiteness conditions guaranteeing joint subnormality semigroup composition operators supplied finally radon nikodym derivatives associated jointly subnormal semigroup composition operators shown laplace transforms probability measures modulo group scalars constituting measurable family
Affiliations des auteurs :
Piotr Budzy/nski 1 ; Jan Stochel 2
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author = {Piotr Budzy/nski and Jan Stochel},
title = {Joint subnormality of $n$-tuples and
$C_0$-semigroups of composition operators on $L^2$-spaces},
journal = {Studia Mathematica},
pages = {167--184},
publisher = {mathdoc},
volume = {179},
number = {2},
year = {2007},
doi = {10.4064/sm179-2-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm179-2-4/}
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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. Studia Mathematica, Tome 179 (2007) no. 2, pp. 167-184. doi: 10.4064/sm179-2-4
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