Jaramillo Aguado, Jesús ÁngelGarrido Carballo, María IsabelGonzález Llavona, José Luis2023-06-202023-06-202005-06-05Garrido, 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.2005.01.015.0166-864110.1016/j.topol.2005.01.015https://hdl.handle.net/20.500.14352/49982Research 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).engjournal articlehttps://doi.org/10.1016/j.topol.2005.01.015http://www.sciencedirect.comhttp://www.sciencedirect.com/science/article/pii/S0166864105000167restricted access515.1Banach spacePolynomial topologiesWeakly convergent sequencesDunford–Pettis propertyTopología1210 Topología