caa a22 4500 386360693 CHVBK 20180307111914.0 cr unu---uuuuu 161130e198906 xx s 000 0 eng 10.1017/S0004972700003221 doi S0004972700003221 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700003221 Becker Richard Equipe d'Analyse, Universite Paris VI, Tour 46 4ème Etage, 4, Place Jussieu, 75252 - Paris Cedex 05, France Sur les cones (faiblement complets) contenus dans le dual d'un espace de Banach non-reflexif [Elektronische Daten] [Richard Becker] Let B be a Banach space. consider the convex proper weakly complete cones X contained in B′ with σ(B′, B) such that X B′, is conic in the sense of Asimow: that is, there exists α ≥ 0 and f B″ such that B ≤ f ≤ α· B on X. This class arises in the theory of integral representations. If B is reflexive, such a cone has a weakly-compact basis. This paper considers the converse problem:- if one requires that X B′1 be σ(B′, B) metrisable, the existence of X (without a compact σ(B′, B) basis) is equivalent to the statement that B is not a Grothendieck space. However, in every space C(K) with infinitely compact K, one can find such a cone X. If two such cones in B′ are not too far apart, their sum belongs to this class. Copyright © Australian Mathematical Society 1989 Bulletin of the Australian Mathematical Society Cambridge University Press 39/3(1989-06), 321-328 0004-9727 39:3<321 1989 39 BAZ https://doi.org/10.1017/S0004972700003221 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700003221 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Becker Richard Equipe d'Analyse, Universite Paris VI, Tour 46 4ème Etage, 4, Place Jussieu, 75252 - Paris Cedex 05, France NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 39/3(1989-06), 321-328 0004-9727 39:3<321 1989 39 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence SWISSBIB 386360693 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge