Topological Dual Systems for Spaces of Vector Measure p-Integrable Functions
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...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/3763649 |
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| _version_ | 1832549323624153088 |
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| author | P. Rueda E. A. Sánchez Pérez |
| author_facet | P. Rueda E. A. Sánchez Pérez |
| author_sort | P. Rueda |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a22e61ac276045fa9ccaa8d40cfa8e74 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-a22e61ac276045fa9ccaa8d40cfa8e742025-02-03T06:11:38ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/37636493763649Topological Dual Systems for Spaces of Vector Measure p-Integrable FunctionsP. Rueda0E. A. Sánchez Pérez1Departamento de Análisis Matemático, Universidad de Valencia, Burjassot, 46100 Valencia, SpainInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, SpainWe 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.http://dx.doi.org/10.1155/2016/3763649 |
| spellingShingle | P. Rueda E. A. Sánchez Pérez Topological Dual Systems for Spaces of Vector Measure p-Integrable Functions Journal of Function Spaces |
| title | Topological Dual Systems for Spaces of Vector Measure p-Integrable Functions |
| title_full | Topological Dual Systems for Spaces of Vector Measure p-Integrable Functions |
| title_fullStr | Topological Dual Systems for Spaces of Vector Measure p-Integrable Functions |
| title_full_unstemmed | Topological Dual Systems for Spaces of Vector Measure p-Integrable Functions |
| title_short | Topological Dual Systems for Spaces of Vector Measure p-Integrable Functions |
| title_sort | topological dual systems for spaces of vector measure p integrable functions |
| url | http://dx.doi.org/10.1155/2016/3763649 |
| work_keys_str_mv | AT prueda topologicaldualsystemsforspacesofvectormeasurepintegrablefunctions AT easanchezperez topologicaldualsystemsforspacesofvectormeasurepintegrablefunctions |