The Levy-Steinitz rearrangement theorem for duals of metrizable spaces

1999/08/20 by Jose Bonet, Bonet, Jose, Andreas Defant +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.math/9908112

arxiv created 1999/08/20 · arxiv updated 2009/11/30

Abstract

Extending the classical Levy-Steinitz rearrangement theorem, which in turn extended Riemann's theorem, Banaszczyk proved in 1990/93 that a metrizable, locally convex space is nuclear if and only if the domain of sums of every convergent series (i.e. the set of all elements in the space which are sums of a convergent rearrangement of the series) is a translate of a closed subspace of a special form. In this paper we present an apparently complete analysis of the domains of convergent series in duals of metrizable spaces or, more generally, in (DF)-spaces in the sense of Grothendieck.

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