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

• Autorzy: Piotr Budzyński , Jan Stochel
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 20M20: Semigroups of transformations, etc.
• 47D03: Groups and semigroups of linear operators
• 47B33: Composition operators
• 47B20: Subnormal operators, hyponormal operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 193
• Numer: 1
• Strony: 29-52

Daty

wydano

2009

Twórcy

autor

Piotr Budzyński

• Katedra Zastosowań Matematyki, Uniwersytet Rolniczy w Krakowie, Al. Mickiewicza 24/28, 30-059 Kraków, Poland

autor

Jan Stochel

• Instytut Matematyki, Uniwersytet Jagielloński, ul. Łojasiewicza 6, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/sm193-1-2