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

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/0901.1771

or

http://arXiv.org/abs/0901.1771

or by email in unzipped form by transmitting an empty message with subject line

uget 0901.1771

or in gzipped form by using subject line

get 0901.1771

to: math@arXiv.org.