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A Pettis-type integral and applications to transition semigroups

Markus Kunze (2011)

Czechoslovak Mathematical Journal

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....

A Riesz representation theory for completely regular Hausdorff spaces and its applications

Marian Nowak (2016)

Open Mathematics

Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let Cb(X, E) be the space of all E-valued bounded, continuous functions on X, equipped with the strict topology β. We develop the Riemman-Stieltjes-type Integral representation theory of (β, || · ||F) -continuous operators T : Cb(X, E) → F with respect to the representing Borel operator measures. For X being a k-space, we characterize strongly bounded (β, || · ||F)-continuous operators T : Cb(X, E) → F. As an application, we...

A scalar Volterra derivative for the PoU-integral

V. Marraffa (2005)

Mathematica Bohemica

A weak form of the Henstock Lemma for the P o U -integrable functions is given. This allows to prove the existence of a scalar Volterra derivative for the P o U -integral. Also the P o U -integrable functions are characterized by means of Pettis integrability and a condition involving finite pseudopartitions.

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