6533b824fe1ef96bd12816a9
RESEARCH PRODUCT
Topological Dual Systems for Spaces of Vector Measure p-Integrable Functions
Pilar RuedaE. A. Sánchez Pérezsubject
Article Subject0211 other engineering and technologies02 engineering and technologyTopologyComputer Science::Digital Libraries01 natural sciencesTopological vector spaceVector measureLocally convex topological vector spaceUnconditional convergenceIntegrable function0101 mathematicsLp spaceCompact convergenceMathematicsPointwise convergence021103 operations researchWeak convergenceTopological duallcsh:Mathematics010102 general mathematicslcsh:QA1-939AlgebraComputer Science::Mathematical SoftwareMATEMATICA APLICADAModes of convergenceAnalysisdescription
[EN] We show a Dvoretzky-Rogers type theorem for the adapted version of the q-summing operators to the topology of the convergence of the vector valued integrals on Banach function spaces. In the pursuit of this objective we prove that the mere summability of the identity map does not guarantee that the space has to be finite dimensional, contrary to the classical case. Some local compactness assumptions on the unit balls are required. Our results open the door to new convergence theorems and tools regarding summability of series of integrable functions and approximation in function spaces, since we may find infinite dimensional spaces in which convergence of the integrals, our vector valued version of convergence in the weak topology, is equivalent to the convergence with respect to the norm. Examples and applications are also given.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-01-01 |