### Impacto

Garrido Carballo, M. Isabel and Jaramillo Aguado, Jesús Ángel and Llavona, José G.
(2005)
*Polynomial topologies on Banach spaces.*
Topology and its Applications, 153
.
pp. 854-867.
ISSN 0166-8641

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Official URL: http://www.sciencedirect.com/science/article/pii/S0166864105000167

## Abstract

On every real Banach space X we introduce a locally convex topology tau(p), canonically associated to the weak-polynomial topology w(P). It is proved that tau(p) is the finest locally convex topology on X which is coarser than w(P). Furthermore, the convergence of sequences is considered, and sufficient conditions on X are obtained under which the convergent sequences for w(P) and for tau(P) either coincide with the weakly convergent sequences (when X has the Dunford-Pettis property) or coincide with the norm-convergent sequences (when X has nontrivial type).

Item Type: | Article |
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Uncontrolled Keywords: | Banach space; Polynomial topologies; Weakly convergent sequences; Dunford–Pettis property |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 15509 |

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Deposited On: | 07 Jun 2012 08:31 |

Last Modified: | 06 Feb 2014 10:26 |

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