RT Book, Section
T1 Bounded duality in topological abelian groups
A1 Martín Peinador, Elena
A1 Chasco, M. J.
A2 Amigó, J. M.
A2 Cánovas, M. J.
A2 López-Cerdá, M. A.
A2 López-Pellicer, M.
AB We define the β-duality for topological Abelian groups by means of the notion of Hejcman of boundedness in uniform spaces. A real locally convex space considered as an Abelian topological group is β-reflexive iff it is reflexive in the ordinary sense for locally convex spaces. Thus, β-reflexivity is the natural extension to Abelian topological groups of the well-known notion of reflexivity. We prove: 1) A locally compact Abelian group is β-reflexive. 2) A β-reflexive metrizable group is reflexive in Pontryagin sense. 3) The β-bidual of a metrizable group is also a metrizable group.
PB Springer
YR 2023
FD 2023-07-02
LK https://hdl.handle.net/20.500.14352/87220
UL https://hdl.handle.net/20.500.14352/87220
LA eng
DS Docta Complutense
RD 9 abr 2025