On shifts of sequences
type: Item
instance of: scholarly article
title: On shifts of sequences
zbMATH Open document ID: 0629.46006
DOI: 10.1007/BF01907704
author: Yu. F. Korobeinik
published in: Analysis Mathematica
publication date: 1986-01-01T00:00:00Z
review text: A sequence \(X=(x_ k)_{k\in {\mathbb{N}}}\) in a topological vector space E is called complete if \(\overline{span}\{x_ k\}=E\) and representing if every \(y\in E\) can be represented as \(x=\sum^{\infty}_{k=1}c_ kx_ k\) for suitable scalars \(c_ k.\) If E is separable it is shown that these two properties are inherited by the shifted sequence \((x_{k+1})_{k\in {\mathbb{N}}}\) iff \(E'=\{0\}\).
Mathematics Subject Classification ID: 46A35
Mathematics Subject Classification ID: 46A20
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 4023999
zbMATH Keywords: complete sequence
zbMATH Keywords: representing sequence
zbMATH Keywords: dual space
zbMATH Keywords: shifted sequence
reviewed by: Wolfgang Arendt
MaRDI profile type: Publication
cites work: On Absolutely Convergent Exponential Sums
cites work: Q3227843
cites work: The Brauer-Manin Obstruction and III[2]
cites work: Q3506242
cites work: Q3052785
full work available at URL: https://doi.org/10.1007/bf01907704
OpenAlex ID: W368958348
description: scientific article; zbMATH DE number 4023999