The Levy-Steinitz rearrangement theorem for duals of metrizable spaces

Bonet, Jose; Defant, Andreas
Bibliographical reference

eprint arXiv:math/9908112

Advertised on:
8
1999
Number of authors
2
IAC number of authors
0
Citations
0
Refereed citations
0
Description
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.