[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j150749

BOUNDED CONVERGENCE THEOREMS

Niemiec, Piotr (Instytut Matematyki, Wydzial Matematyki i Informatyki Uniwersytet Jagiellonski)

Publication Information

Journal of the Korean Mathematical Society / v.54, no.1, 2017 , pp. 319-357 More about this Journal

Abstract

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions in a way such that uniformly bounded sequences of functions that converge pointwise in the weak (or norm) topology of E are sent to sequences that converge in the weak, norm or weak* topology of the target space. As an application, a new description of uniform closures of convex subsets of C(X, E) is given. Also new and strong results on integral representations of continuous linear operators defined on C(X, E) are presented. A new classes of vector measures are introduced and various bounded convergence theorems for them are proved.

Keywords

vector measure; dual Banach space; Riesz characterisation theorem; weakly sequentially complete Banach space; dominated convergence theorem; bounded convergence theorem; function space;

Citations & Related Records

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