The Josefson-Nissenzweig property for locally convex spaces

Taras Banakh, Saak Gabriyelyan

Research output: Working paper/PreprintPreprint

25 Downloads (Pure)

Abstract

We define a locally convex space E to have the Josefson-Nissenzweig property (JNP) if the identity map (E′,σ(E′,E))→(E′,β∗(E′,E)) is not sequentially continuous. By the classical Josefson-Nissenzweig theorem, every infinite-dimensional Banach space has the JNP. A characterization of locally convex spaces with the JNP is given. We thoroughly study the JNP in various function spaces. Among other results we show that for a Tychonoff space X, the function space Cp(X) has the JNP iff there is a weak∗ null-sequence (μn)n∈ω of finitely supported sign-measures on X with unit norm. However, for every Tychonoff space X, neither the space B1(X) of Baire-1 functions on X nor the free locally convex space L(X) over X has the JNP.
Original languageEnglish
StatePublished - 2020

Keywords

  • math.FA
  • math.GN
  • 46A03

Fingerprint

Dive into the research topics of 'The Josefson-Nissenzweig property for locally convex spaces'. Together they form a unique fingerprint.

Cite this