Please use this identifier to cite or link to this item:
http://hdl.handle.net/10662/12921
Title: | On sequentially right Banach spaces |
Authors: | Kačena, Miroslav |
Keywords: | Weakly compact operator;Right topology;Dunford-Pettis property;Property (V);Dieudonn´e property;Operador débilmente compacto;Topología derecha;Propiedad Dunford-Pettis;Propiedad (V);Propiedad de Dieudonné |
Issue Date: | 2011 |
Publisher: | Universidad de Extremadura, Servicio de Publicaciones |
Abstract: | In this paper, we study the recently introduced class of sequentially Right Banach spaces. We introduce a stronger property (RD) and compare these two properties with other well-known isomorphic properties of Banach spaces such as property (V) or the Dieudonné property. In particular, we show that there is a sequentially Right Banach space without property (V). This answers a question of A.M. Peralta, I. Villanueva, J.D.M. Wright and K. Ylinen. We also generalize a result of A. Pelczy´nski and prove that every sequentially Right Banach space has weakly sequentially complete dual. Finally, it is shown that if K is a scattered compact Hausdorff space then the space C(K;X) of X-valued continuous functions on K is sequentially Right (resp. has property (RD)) if and only if X has the same property. |
URI: | http://hdl.handle.net/10662/12921 |
ISSN: | 0213-8743 |
Appears in Collections: | Extracta Mathematicae Vol. 26, nº 1 (2011) |
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2605-5686_26_1_1.pdf | 171,06 kB | Adobe PDF | View/Open |
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