Approximative compactness and full rotundity in Musielak–Orlicz spaces and Lorentz–Orlicz spaces
Copyright policy )Approximative compactness and full rotundity in Musielak–Orlicz spaces and Lorentz–Orlicz spaces
We prove that approximative compactness of a Banach space X is equivalent to the conjunction of reflexivity and the Kadec–Klee property of X . This means that approximative compactness coincides with the drop property defined by Rolewicz in Studia Math. 85 (1987), 25–35. Using this general result we find criteria for approximative compactness in the class of Musielak–Orlicz function and sequence spaces for both (the Luxemburg norm and the Amemiya norm) as well as critria for this property in the class of Lorentz–Orlicz spaces. Criteria for full rotundity of Musielak–Orlicz spaces are also presented in the case of the Luxemburg norm. An example of a reflexive strictly convex Köthe function space which is not approximatively compact and some remark concerning the compact faces property for Musielak–Orlicz spaces are given.
- Adam Mickiewicz University in Poznań Poland
- Jagiellonian University Poland
Banach lattices, Musielak-Orlicz spaces, reflexivity, Amemyia norm, Luxemburg norm, approximative compactness, Lorentz-Orlicz spaces, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), full rotundity, Geometry and structure of normed linear spaces, drop property, Kadec-Klee property, Amemiya norm, Banach sequence spaces, Ordered normed spaces
Banach lattices, Musielak-Orlicz spaces, reflexivity, Amemyia norm, Luxemburg norm, approximative compactness, Lorentz-Orlicz spaces, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), full rotundity, Geometry and structure of normed linear spaces, drop property, Kadec-Klee property, Amemiya norm, Banach sequence spaces, Ordered normed spaces
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