RT Journal Article
T1 On Banach-Spaces Of Vector-Valued Continuous-Functions
A1 Cembranos, Pilar
AB Let K tie a compact Hausdorff space and let E be a BanachSpace. We denote by C(K, E) the Banach space of all E-valuedContinuous functions defined on K , endowed with the supremum Norm.Recently, Talagrand [Israel J. Math. 44 (1983), 317-321]Constructed a Banach space E having the Dunford-Pettis propertySuch that C([0, l ] , E) fails to have the Dunford-Pettis property.So he answered negatively a question which was posed some years ago.We prove in this paper that for a large class of compacts K(the scattered compacts), C(K, E) has either the Dunford-PettisProperty, or the reciprocal Dunford-Pettis property, or theDieudonne property, or property V if and only if E has theSame property.Also some properties of the operators defined on C(K, E) areStudied.
PB Australian Mathematics Publ
SN 0004-9727
YR 1983
FD 1983
LK https://hdl.handle.net/20.500.14352/64615
UL https://hdl.handle.net/20.500.14352/64615
LA eng
DS Docta Complutense
RD 10 may 2025