Nonlinear centralizers with values in \(L_0\)
type: Item
instance of: scholarly article
title: Nonlinear centralizers with values in \(L_0\)
zbMATH Open document ID: 1306.46026
author: Félix Cabello Sánchez
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2014-01-16T00:00:00Z
review text: A function space is defined here as a linear subspace of \(L_0\), equipped with an \(F\)-norm which makes the embedding continuous. Such spaces carry a natural structure as modules over \(L_\infty\) (think of pointwise multiplication), and are considered in this category in all the following statements. Centralizers between function spaces form a class of quasilinear maps which arise in various situations; they include all maps which are continuous at the origin. In the case of maps into \(L_0\), it is proved that there are no others. One application is that, if \(L_\infty\) is dense in a function space \(X\) (in particular if \(X=L_0\)), then every twisted sum of \(L_0\) and \(X\) is trivial. Another is the existence of an Orlicz space \(L_N\) for which there is a non-trivial twisted sum of \(L_N\) and \(L_N^*\), even though the only homomorphism from \(L_N^*\) to \(L_N\) is \(0\).
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46M18
Mathematics Subject Classification ID: 46A16
zbMATH DE Number: 6246141
zbMATH Keywords: function space
zbMATH Keywords: centralizer
zbMATH Keywords: twisted sum
MaRDI profile type: Publication
full work available at URL: j.na.2013.04.006
OpenAlex ID: W2129021848
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DOI: 10.1016/J.NA.2013.04.006
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description: scientific article; zbMATH DE number 6246141