Affiliation:
1. Ivan Franko National University of Lviv, Ukraine + Jan Kochanowski University in Kielce, Poland
2. Department of Mathematics, Ben-Gurion University of the Negev, Israel
Abstract
We define a locally convex space E to have the Josefson-Nissenzweig property
(JNP) if the identity map (E?, ?(E?, E)) ? (E?, ?*(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 (?n)n?? 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.
Publisher
National Library of Serbia
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