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Polynomial topologies on Banach spaces Jaramillo Aguado, Jesús Ángel Garrido Carballo, María Isabel González Llavona, José Luis 515.1 Banach space Polynomial topologies Weakly convergent sequences Dunford–Pettis property Topología 1210 Topología Research supported in part by DGES (Spain) with grants BFM2000-0609 and BFM2003-06420 2005 Elsevier B.V. All rights reserved. It is a great pleasure to thank Professors Silvia Lassalle, Juan Ferrera and Angeles Prieto for several valuable conversations concerning this work. 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). DGES (Spain) Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T09:35:29Z 2023-06-20T09:35:29Z 2005-06-05 journal article https://hdl.handle.net/20.500.14352/49982 0166-8641 10.1016/j.topol.2005.01.015 eng Garrido, M. Isabel, et al. «Polynomial Topologies on Banach Spaces». Topology and Its Applications, vol. 153, n.o 5-6, diciembre de 2005, pp. 854-67. DOI.org (Crossref), https://doi.org/10.1016/j.topol.2005.01.015. restricted access application/pdf Elsevier Science