On rearrangements of series in locally convex spaces
type: Item
instance of: scholarly article
title: On rearrangements of series in locally convex spaces
zbMATH Open document ID: 0890.40001
author: M. J. Chasco
author: Sergei Chobanyan
published in: Michigan Mathematical Journal
publication date: 1998-03-11T00:00:00Z
review text: This paper deals with the structure of the set of sums of a conditionally convergent series in locally convex metrizable topological vector spaces. The problem goes back to the well-known theorem in analysis due to Riemann asserting that the set of sums \({\mathcal S}_{(a_k)}\) of a conditionally convergent series \(\sum^\infty_{k=1} a_k\), \(a_k\in \mathbb{R}\), under all its convergent rearrangements fills the whole real line \(\mathbb{R}\). This was generalized to the case of finite-dimensional spaces by Levy and Steinitz.
Mathematics Subject Classification ID: 40J05
Mathematics Subject Classification ID: 46A35
zbMATH DE Number: 1127775
zbMATH Keywords: conditionally convergent series
zbMATH Keywords: locally convex metrizable topological vector spaces
zbMATH Keywords: convergent rearrangements
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029005791
OpenAlex ID: W2055020983
DOI: 10.1307/MMJ/1029005791
description: scientific article; zbMATH DE number 1127775