caa a22 4500 467882770 CHVBK 20180406152725.0 cr unu---uuuuu 170328e20060401xx s 000 0 eng 10.1007/s10485-005-9005-4 doi (NATIONALLICENCE)springer-10.1007/s10485-005-9005-4 Every Banach Space is Reflexive [Elektronische Daten] [Christophe Van Olmen, Stijn Verwulgen] The title above is wrong, because the strong dual of a Banach space is too strong to assert that the natural correspondence between a space and its bidual is an isomorphism. However, for many applications it suffices to replace the norm on the first dual by the weak*-structure in order to solve the non-reflexiveness problem [1]. But in this way, only the original vector space is recovered by taking the second dual. In this work we introduce a suitable numerical structure on vector spaces such that Banach balls, or more precisely totally convex modules, arise naturally in duality, namely as a category of Eilenberg-Moore algebras. This numerical structure naturally overlies the weak*-topology on the algebraic dual, so the entire Banach space can be reconstructed as a second dual. Moreover, the isomorphism between the original space and its bidual is the unit of an adjunction between the two-dualisation functors. Notice that the weak*-topology is normable only if it lives on a finite dimensional space; in that case the original space is trivial as well, hence reflexive. So the overlying numerical structure should be something more general than a norm or a seminorm and thus approach theory [2, 3] enters the picture. Springer Science+Business Media, Inc., 2006 locally convex approach space nationallicence duality nationallicence totally convex module nationallicence Banach space nationallicence weak*-structure nationallicence Van Olmen Christophe Department of Mathematics, University of Antwerp, Middleheimlaan 1, 2020, Antwerp, Belgium aut Verwulgen Stijn Department of Mathematics, University of Antwerp, Middleheimlaan 1, 2020, Antwerp, Belgium aut Applied Categorical Structures Kluwer Academic Publishers 14/2(2006-04-01), 123-134 0927-2852 14:2<123 2006 14 10485 https://doi.org/10.1007/s10485-005-9005-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-005-9005-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Van Olmen Christophe Department of Mathematics, University of Antwerp, Middleheimlaan 1, 2020, Antwerp, Belgium aut NATIONALLICENCE 700 1- Verwulgen Stijn Department of Mathematics, University of Antwerp, Middleheimlaan 1, 2020, Antwerp, Belgium aut NATIONALLICENCE 773 0- Applied Categorical Structures Kluwer Academic Publishers 14/2(2006-04-01), 123-134 0927-2852 14:2<123 2006 14 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer