A General Pettis Integral and Applications to Transition Semigroups

Details A General Pettis Integral and Applications to Transition Semigroups A General Pettis Integral and Applications to Transition Semigroups

2009-01-13

arxiv.org/abs/0901.1771v1

Mathematics

Functional Analysis

19 pages, no figures

Scientific paper

Motivated by applications to transition semigroups, we introduce the notion of a norming dual pair and study a Pettis-type integral on such pairs. In particular, we establish a sufficient condition for integrability. We also introduce and study a class of semigroups on such dual pairs which are an abstract version of transition semigroups. Using our results, we prove conditions ensuring that a semigroup consisting of kernel operators is Laplace transformable such that the Laplace transform consists of kernel operators again.

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