In the previous paper, we have characterized (joint) subnormality of a C₀-semigroup of composition operators on L²-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 C₀-groups of composition operators on L²-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 C₀-semigroups of composition operators on L²-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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-1-2,
author = {Piotr Budzy\'nski and Jan Stochel},
title = {Joint subnormality of n-tuples and C0-semigroups of composition operators on L2-spaces, II},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {29-52},
zbl = {1173.47014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-1-2}
}
Piotr Budzyński; Jan Stochel. Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces, II. Studia Mathematica, Tome 192 (2009) pp. 29-52. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-1-2/