Permutations of series in infinite-dimensional spaces
type: Item
instance of: scholarly article
title: Permutations of series in infinite-dimensional spaces
zbMATH Open document ID: 0707.40001
DOI: 10.1007/BF01158621
author: I. Barani
published in: Mathematical Notes
publication date: 1989-01-01T00:00:00Z
review text: Let X be a linear space and \(A=\{a_ n\}_ 1^{\infty}\) a sequence of elements of X. Denote by S(A) the set of all \(x\in X\) having the form \(x=\sum^{\infty}_{n=1}a_{g(n)}\), where g is a permutation of the set \({\mathbb{N}}=\{1,2,...\}\). If X is finite-dimensional then S(A) is a linear variety [cf. \textit{E. Steinitz}, Bedingt konvergente Reihen und konvexe Systeme, J. Reine Angew. Math. 143, 128-175 (1913)]. In the case of infinite-dimensional X the author gives sufficient conditions for the set S(A) to be a closed linear variety.
Mathematics Subject Classification ID: 40A05
zbMATH DE Number: 4161338
zbMATH Keywords: linear variety
reviewed by: Tibor Šalát
MaRDI profile type: Publication
cites work: Balancing matrices with line shifts
cites work: Über das Umordnungsproblem im Hilbertschen Raum
cites work: Q5817584
cites work: Q5827077
cites work: Q3910875
description: scientific article; zbMATH DE number 4161338