Pettis integration in locally convex spaces

Ali, Sk. Jaker; Chakraborty, N. D.; али, Ск. Якер; Чакраборти, Н. Л.

doi:10.1007/bf02789840

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2011

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Cited by 8 publications

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“…It should be noted that the Y -integral actually coincides with the Pettis integral on the locally convex space (X, τ ), for any locally convex topology τ on X such that (X, τ ) ′ = Y . However, in contrast to conditions for Pettis integrability on locally convex spaces, see [13], our condition is more in the spirit of the characterization of Bochner integrability and the proof makes extensive use of the norm topologies on X and Y .…”

Section: Introductionmentioning

confidence: 99%

A Pettis-type integral and applications to transition semigroups

Kunze

2011

Czech Math J

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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 give conditions ensuring that a semigroup consisting of kernel operators has a Laplace transform which also consists of kernel operators. We also provide conditions under which a semigroup is uniquely determined by its Laplace transform.

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Section: Introductionmentioning

confidence: 99%