Non absolutely convergent integrals of functions taking values in a locally convex space

Properties of McShane and Kurzweil-Henstock integrable functions taking values in a locally convex space are considered and the relations with other integrals are studied. A convergence theorem for the Kurzweil-Henstock integral is give

A characterization of absolutely summing operators by means of McShane integrable functions

Absolutely summing operators between Banach spaces are characterized by means of Mc-Shane integrable function

Stieltjes Differential Inclusions with Periodic Boundary Conditions without Upper Semicontinuity

We are studying first order differential inclusions with periodic boundary conditions where the Stieltjes derivative with respect to a left-continuous non-decreasing function replaces the classical derivative. The involved set-valued mapping is not assumed to have compact and convex values, nor to be upper semicontinuous concerning the second argument everywhere, as in other related works. A condition involving the contingent derivative relative to the non-decreasing function (recently introduced and applied to initial value problems by R.L. Pouso, I.M. Marquez Albes, and J. Rodriguez-Lopez) is imposed on the set where the upper semicontinuity and the assumption to have compact convex values fail. Based on previously obtained results for periodic problems in the single-valued cases, the existence of solutions is proven. It is also pointed out that the solution set is compact in the uniform convergence topology. In particular, the existence results are obtained for periodic impulsive differential inclusions (with multivalued impulsive maps and finite or possibly countable impulsive moments) without upper semicontinuity assumptions on the right-hand side, and also the existence of solutions is derived for dynamic inclusions on time scales with periodic boundary conditions

Convergence for varying measures in the topological case

In this paper convergence theorems for sequences of scalar, vector and multivalued Pettis integrable functions on a topological measure space are proved for varying measures vaguely convergent.Comment: 19 page

Product local system and Fubini and Tonelli theorems

We present an integral, called S-integral, de ned by means of Riemann sums related to product local systems on the plane. The classical Henstock integral on the plane with respect to the Kurzweil basis is an example of integral related to a product local system. Some properties and a Fubini type theorem for the S-integral are considered. A monotone convergence theorem for the integral constructed by a local sys- tem in the real line is given and it is used to obtain a Tonelli type theorem for a product local system

A characterization of strongly measurable Henstock-Kurzweil integrable functions and weakly continuous operators

We give necessary and sufficient conditions for the Kurzweil–Henstock integrability of functions given by f =n=1 xnχEn , where xn belong to a Banach space and the sets (En)n are measurable and pairwise disjoint. Also weakly completely continuous operators between Banach spaces are characterized by means of scalarly Kurzweil–Henstock integrable function

MR2374457 (2009j:28033) Kakihara, Yûichirô Integration with respect to Hilbert-Schmidt class operator valued measures. Applied functional analysis, 263--278, Yokohama Publ., Yokohama, 2007. (Reviewer: Valeria Marraffa)

Integration with respect to Hilbert-Schmidt class operator valued measure