On \(\mathcal L_{\infty}\)-envelopes of Banach spaces
type: Item
instance of: scholarly article
title: On \(\mathcal L_{\infty}\)-envelopes of Banach spaces
zbMATH Open document ID: 1253.46005
author: Jesús Suárez
author: Jesús M. F. Castillo
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-08-01T00:00:00Z
review text: Given a reasonable class of Banach spaces \({\mathcal A}\), and an arbitrary Banach space \(X\), can one always find an \({\mathcal A}\)-space \(Y\) containing \(X\), so that every operator from \(X\) into an \({\mathcal A}\)-space admits a norm preserving extension to \(Y\)? This is well known for the class of \(L_\infty(\mu)\) spaces. Here it is shown that the conclusion holds for the most interesting classes of \({\mathcal L}_\infty\) spaces. This is established by devising a flexible construction, which not only unifies several known cases (\(C(K)\) spaces, Lindenstrauss spaces, \({\mathcal L}_{\infty,\lambda}\) spaces), but also yields some new cases (\(\lambda\)-separably-injective spaces, universally \(\lambda\)-separably-injective spaces, \(\lambda\)-Lindenstrauss-Pełczyński spaces).
Mathematics Subject Classification ID: 46A22
Mathematics Subject Classification ID: 46B26
Mathematics Subject Classification ID: 46M18
zbMATH DE Number: 6062809
zbMATH Keywords: extension of operators
zbMATH Keywords: \({\mathcal L}_\infty\)-spaces
MaRDI profile type: Publication
full work available at URL: j.jmaa.2012.04.034
OpenAlex ID: W1995686404
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DOI: 10.1016/J.JMAA.2012.04.034
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description: scientific article; zbMATH DE number 6062809