Orthomorphisms on non-Banach \(F\)-lattices containing a copy of \(\mathbb{R}^{\mathbb{N}}\) with applications to Musielak-Orlicz spaces
type: Item
instance of: scholarly article
title: Orthomorphisms on non-Banach \(F\)-lattices containing a copy of \(\mathbb{R}^{\mathbb{N}}\) with applications to Musielak-Orlicz spaces
zbMATH Open document ID: 1383.46005
author: M. Wójtowicz
author: Halina Wiśniewska
published in: Journal of Mathematical Analysis and Applications
publication date: 2017-11-02T00:00:00Z
review text: In the framework of topological linear lattices and their properties, the authors consider (non-Banach) \(F\)-lattices with the sigma-Fatou property. They prove that, if one such space contains a subspace linearly homeomorphic to the \(F\)-lattice \(\omega\) of the sequences of real numbers, the lattice of all its orthomorphisms contains a linear-lattice copy of \(\omega\). In particular, \(\mathrm{Orth}(E)\) contains noncentral orthomorphisms. In the case of Musielak-Orlicz \(F\)-lattices, they show that this property can be expressed by means of a property of Musielak-Orlicz functions.
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 06B30
Mathematics Subject Classification ID: 46B42
Mathematics Subject Classification ID: 54F05
zbMATH DE Number: 6802344
zbMATH Keywords: linear lattice
zbMATH Keywords: \(F\)-lattice
zbMATH Keywords: orthomorphism
zbMATH Keywords: Musielak-Orlicz space
reviewed by: Esteban Induraín
MaRDI profile type: Publication
full work available at URL: j.jmaa.2017.09.044
OpenAlex ID: W2758674729
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DOI: 10.1016/J.JMAA.2017.09.044
description: scientific article; zbMATH DE number 6802344