A positive answer to the basis problem
type: Item
instance of: scholarly article
title: A positive answer to the basis problem
zbMATH Open document ID: 0930.46016
DOI: 10.1007/BF02897059
author: Paolo Terenzi
published in: Israel Journal of Mathematics
publication date: 2000-02-09T00:00:00Z
review text: Let \(X\) be a separable Banach space. There are given various definitions of bases \((x_n)\) in \(X\), where \(x_n\in X\) for \(n= 1,2,\dots\)\ . Among else there is defined the uniformly minimal basis \((x_n)\) with quasi-fixed brackets and permutations, denoted in the following by \((D_4)\). The paper is devoted to proofs of the following fundamental two theorems: 1) Every separable Banach space has a \((D_4)\)-basis. 2) Every subspace of a separable Banach space \(X\) has a \((D_4)\)-basis which can be extended to a \((D_4)\)-basis of \(X\).
Mathematics Subject Classification ID: 46B15
zbMATH DE Number: 1251443
zbMATH Keywords: biorthogonal system
zbMATH Keywords: uniformly minimal basis with quasi-fixed brackets and permutations
reviewed by: Julian Musielak
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02897059
OpenAlex ID: W2070591252
description: scientific article; zbMATH DE number 1251443