Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces, II

Piotr Budzyński, and Jan Stochel. "Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces, II." Studia Mathematica 193.1 (2009): 29-52. <http://eudml.org/doc/284490>.

@article{PiotrBudzyński2009,
abstract = {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.},
author = {Piotr Budzyński, Jan Stochel},
journal = {Studia Mathematica},
keywords = {composition operator on -space; -semigroup; -group; subnormal operator; joint subnormality},
language = {eng},
number = {1},
pages = {29-52},
title = {Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces, II},
url = {http://eudml.org/doc/284490},
volume = {193},
year = {2009},
}

TY - JOUR
AU - Piotr Budzyński
AU - Jan Stochel
TI - Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces, II
JO - Studia Mathematica
PY - 2009
VL - 193
IS - 1
SP - 29
EP - 52
AB - 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.
LA - eng
KW - composition operator on -space; -semigroup; -group; subnormal operator; joint subnormality
UR - http://eudml.org/doc/284490
ER -