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Acta Mathematica Hungarica

, Volume 157, Issue 1, pp 254–268 | Cite as

Weak compactness and metrizability of Mackey*-bounded sets in Fréchet spaces

  • J. C. FerrandoEmail author
  • J. Ka̧kol
Article
  • 63 Downloads

Abstract

Motivated by the density condition in the sense of Heinrich for Fréchet spaces and by some results of Schlüchtermann and Wheeler for Banach spaces, we characterize in terms of certain weakly compact resolutions those Fréchet spaces enjoying the property that each bounded subset of its Mackey* dual is metrizable. We also characterize those Köthe echelon Fréchet spaces \({\lambda _{p}(A)}\) as well as those Fréchet spaces Ck (X) of real-valued continuous functions equipped with the compact-open topology that enjoy this property.

Mathematics Subject Classification

primary 46A03 secondary 54A25 54D50 

Key words and phrases

bounded resolution weakly compact resolution \({\mathfrak{G}}\)-base of neighborhoods K-analytic space SWKA space SWCG space 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Centro de Investigación OperativaUniversidad Miguel HernándezElcheSpain
  2. 2.Faculty of Mathematics and InformaticsA. Mickiewicz UniversityPoznańPoland
  3. 3.Institute of Mathematics of the Czech Academy of SciencesPragueCzech Republic

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