This is an announcement for the paper "A general Pettis integral and applications to transition semigroups" by Markus Kunze.
Abstract: 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.
Archive classification: math.FA
Mathematics Subject Classification: 46G10, 47D03, 60J35
Remarks: 19 pages, no figures
The source file(s), pettists.tex: 64277 bytes, is(are) stored in gzipped form as 0901.1771.gz with size 19kb. The corresponding postcript file has gzipped size 122kb.
Submitted from: m.c.kunze@tudelft.nl
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