A special class of Banach spaces
type: Item
instance of: scholarly article
title: A special class of Banach spaces
zbMATH Open document ID: 0574.46010
DOI: 10.1007/BF01158744
author: B. V. Godun
published in: Mathematical Notes
publication date: 1985-01-01T00:00:00Z
review text: Theorem 1. Let \((e_ n)_ 1^{\infty}\) be a Schauder basis in a Banach space E, and \(\Gamma =[e^*_ n]_ 1^{\infty}\) its coefficient space. Then there exists an equivalent norm on E such that every non- separable subspace of \(E^*\) containing \(\Gamma\) does not have Auerbach bases. Theorem 2. There exists a Banach space which has an unconditional basis but does not have Auerbach bases. Theorem 3. Let E be a Banach space with a Schauder basis. Then there exists an equivalent norm on E in which every Auerbach basis is a 1- norming Markushevich basis. A biorthogonal system \((x_ i,x^*_ i)_{i\in I}\) is said to be an Auerbach basis if \((x_ i)_{i\in I}\) is a complete system and \(\| x_ i\| =\| x^*_ i\| =1\), \(i\in I\).
Mathematics Subject Classification ID: 46B15
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 3916982
zbMATH Keywords: Schauder basis
zbMATH Keywords: equivalent norm
zbMATH Keywords: Auerbach bases
zbMATH Keywords: unconditional basis
zbMATH Keywords: 1- norming Markushevich basis
zbMATH Keywords: biorthogonal system
reviewed by: M. I. Kadets
MaRDI profile type: Publication
cites work: Q3920142
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description: scientific article; zbMATH DE number 3916982