Orlicz lattices with modular topology. II. (English) Zbl 0679.46022

(X,\(\rho)\) denotes an Orlicz lattice, where X is a Riesz space, \(\rho\) is a convex modular and \(\tau^{{\hat{\;}}}_{\rho}\) denotes a modular topology. In the first part of the note there are given very interesting properties of the space \((X,\tau^{{\hat{\;}}}_{\rho})\). In the following we have a remark on the associated space and a theorem which says that sequentially modular continuous functionals on Orlicz lattices in \(L^ 0\) have the extension property. Very important are theorems given in the part 4, where the modular topology \(\tau^{{\hat{\;}}}_{\rho}\) on Orlicz spaces \(L^{\phi}\) is considered. The last part of the note contains the various relations between different spaces of linear mappings (between Orlicz lattices). [For part I see the review above.]
Reviewer: A.Waszak


46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46A40 Ordered topological linear spaces, vector lattices
46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators


Zbl 0679.46021
Full Text: EuDML