The Mackey Convergence Condition for Spaces with Webs

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Abstract

If each sequence converging to 0 in a locally convex space is also Mackey convergent to 0, that space is said to satisfy the Mackey convergence condition. The problem of characterizing those locally convex spaces with this property is still open. In this paper, spaces with compatible webs are used to construct both a necessary and a sufficient condition for a locally convex space to satisfy the Mackey convergence condition.

Original languageEnglish
Pages (from-to)473-483
Number of pages11
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume11
Issue number3
DOIs
StatePublished - 1988

Keywords

  • Compatible web
  • Mackey convergent sequence
  • fast complete space
  • inductive limit

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