An extension property of the Bourgain-Pisier construction
type: Item
instance of: scholarly article
title: An extension property of the Bourgain-Pisier construction
zbMATH Open document ID: 1282.46005
author: Jesús Suárez de la Fuente
published in: Arkiv för Matematik
publication date: 2013-09-02T00:00:00Z
review text: Extensions of operators, especially with preservation of the norm, lie at the heart of functional analysis. This paper adds a significant class of examples. If \(X\) is a separable Banach space, \(\mu\geq1\), and \(Y=\mathcal{L}_{\infty,\mu+\varepsilon}(X)\) is a Bourgain-Pisier space associated with \(X\), then every linear operator from \(X\) into any \(\mathcal{L}_{\infty,\mu}\) space admits a norm preserving extension to \(Y\). This is really nontrivial since, for example, \(Y/X\) has the Schur property.
Mathematics Subject Classification ID: 46A22
Mathematics Subject Classification ID: 46B28
zbMATH DE Number: 6203782
zbMATH Keywords: norm preserving extension
zbMATH Keywords: Bourgain-Pisier space
MaRDI profile type: Publication
full work available at URL: s11512-012-0166-8
OpenAlex ID: W2015707258
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DOI: 10.1007/S11512-012-0166-8
description: scientific article; zbMATH DE number 6203782