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Polynomial topologies on Banach spaces


Garrido, 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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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
Uncontrolled Keywords:Banach space; Polynomial topologies; Weakly convergent sequences; Dunford–Pettis property
Subjects:Sciences > Mathematics > Topology
ID Code:15509

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