Orthomorphisms on non-Banach \(F\)-lattices containing a copy of \(\mathbb{R}^{\mathbb{N}}\) with applications to Musielak-Orlicz spaces
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.
scientific article; zbMATH DE number 6802344
scientific article