RT Journal Article
T1 Sequential continuity in the ball topology of a Banach space
A1 Suárez Granero, Antonio
A1 Jiménez Sevilla, María Del Mar
A1 Moreno, José Pedro
AB Consider the isometric property (P): the restriction to the unit ball of every bounded linear functional is sequentially continuous in the ball topology. We present in this paper a systematic study of this property, which is a sequential version of the well known ball generated property. A separable Banach space is Asplund if and only if there exists an equivalent norm with property (P). However, in nonseparable spaces this equivalence does not work. Examples of nonseparable Banach spaces with property (P) which are not Asplund are given. Also, we exhibit a nonseparable Asplund space, namely the space of continuous functions on the Kunen compact, admitting no equivalent norm with this property. We characterize reflexive spaces as those satisfying that every equivalent norm has property (P), thus improving a previous characterization involving the ball generated property. Finally, we investigate the relationships between property (P) and Grothendieck spaces.
PB Elsevier Science
SN 0019-3577
YR 1999
FD 1999-09
LK https://hdl.handle.net/20.500.14352/58649
UL https://hdl.handle.net/20.500.14352/58649
LA eng
NO Suárez Granero, A., Jiménez Sevilla, M. M., Moreno, J. P. «Sequential Continuity in the Ball Topology of a Banach Space». Indagationes Mathematicae, vol. 10, n.o 3, septiembre de 1999, pp. 423-35. DOI.org (Crossref), https://doi.org/10.1016/S0019-3577(99)80033-0.
NO Dirección General de Investigación Científica y Técnica (España)
DS Docta Complutense
RD 12 may 2025