Uniqueness of unconditional and symmetric structures in finite dimensional spaces
type: Item
instance of: scholarly article
title: Uniqueness of unconditional and symmetric structures in finite dimensional spaces
zbMATH Open document ID: 0707.46005
published in: Illinois Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: This paper is a study of uniqueness of symmetric and unconditional bases in a family of finite dimensional Banach spaces (see the paper for a precise definition of these concepts). In general, the results obtained are too highly technical in nature and content to be detailed here. However a major application worth mentioning is that of a rearrangement invariant Banach function space X on [0,1]. In this case, letting \(X_ n\) be those functions which are constant on each atom of the algebra \(B_ n\) generated by the interval [(k-1)/n,k/n), \(1\leq k\leq n\), the family of subspaces \(\{X_ n\}^{\infty}_{n=1}\) is shown to have a unique symmetric basis and an almost unique unconditional basis.
Mathematics Subject Classification ID: 46B15
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 4161427
zbMATH Keywords: uniqueness of symmetric and unconditional bases
zbMATH Keywords: rearrangement invariant Banach function space
author: Peter G. Casazza
author: N. J. Kalton
author: L. A. Tsafriri
reviewed by: James R. Holub
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4161427