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Geometric properties of symmetric spaces with applications to Orlicz-Lorentz spaces. (English) Zbl 0920.46022

Summary: We deal with the basic convexity properties – rotundity, and uniform, local uniform and full rotundity – for symmetric spaces. A characterization of Orlicz-Lorentz spaces with the Kadec-Klee property for pointwise convergence is given. These results are applied to obtain criteria of convexity properties for Orlicz-Lorentz sequence spaces, and some new proofs of the sufficiency part of criteria for rotundity and uniform rotundity for Orlicz-Lorentz function spaces.

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46B42 Banach lattices
46B20 Geometry and structure of normed linear spaces
46A45 Sequence spaces (including Köthe sequence spaces)
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