Martín Peinador, Elena y Chasco, M.J. y Tarieladze, Vaja (1999) On Mackey topology for groups. Studia Mathematica, 132 (3). pp. 257-284. ISSN 0039-3223
Restringido a Sólo personal autorizado del repositorio hasta 31 Diciembre 2020.
|URL||Tipo de URL|
The present paper is a contribution to fill in a gap existing between the theory of topological vector spaces and that of topological abelian groups. Topological vector spaces have been extensively studied as part of Functional Analysis. It is natural to expect that some important and elegant theorems about topological vector spaces may have analogous versions for abelian topological groups. The main obstruction to get such versions is probably the lack of the notion of convexity in the framework of groups. However, the introduction of quasi-convex sets and locally quasi-convex groups by Vilenkin  and the work of Banaszczyk  have paved the way to obtain theorems of this nature. We study here the group topologies compatible with a given duality. We have obtained, among others, the following result: for a complete metrizable topological abelian group, there always exists a finest locally quasi-convex topology with the same set of continuous characters as the original topology. We also give a description of this topology as an G-topology and we prove that, for the additive group of a complete metrizable topological vector space, it coincides with the ordinary Mackey topology.
|Tipo de documento:||Artículo|
|Palabras clave:||locally convex space; Mackey topology; continuous character; weakly compact; locally quasi-convex group; duality.|
|Materias:||Ciencias > Matemáticas > Topología|
|Depositado:||11 Oct 2012 09:01|
|Última Modificación:||07 Feb 2014 09:34|
Descargas en el último año
Sólo personal del repositorio: página de control del artículo