## 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

### MSC:

 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
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