Geometric properties of symmetric spaces with applications to Orlicz-Lorentz spaces

DOI10.1023/A:1009728519669zbMath0920.46022OpenAlexW186392516MaRDI QIDQ1273039

Mieczyslaw Mastylo, Joan L. Cerda, Henryk Hudzik, Anna Kaminska

Publication date: 26 September 1999

Published in: Positivity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1009728519669

zbMATH Keywords

rotundityOrlicz-Lorentz spacesKadec-Klee propertybasic convexity propertiesOrlicz-Lorentz sequence spaces

Mathematics Subject Classification ID

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

Related Items (34)

In some symmetric spaces monotonicity properties can be reduced to the cone of rearrangements ⋮ Uniform Kadec-Klee properties of Orlicz-Lorentz sequence spaces equipped with the Orlicz norm ⋮ Local structure of symmetrizations \(E^{(\ast)}\) with applications ⋮ Isomorphic $\ell ^p$-subspaces in Orlicz-Lorentz sequence spaces ⋮ Relationships between \(K\)-monotonicity and rotundity properties with application ⋮ Orlicz-Lorentz sequence spaces equipped with the Orlicz norm ⋮ Convexity characteristic of Calderón-Lozanovskiĭ sequence spaces ⋮ Non-squareness properties of Orlicz-Lorentz function spaces ⋮ Strongly extreme points in Orlicz-Lorentz function space equipped with the Orlicz norm ⋮ $k$-uniform convexity in Orlicz-Lorentz function space equipped with the Orlicz norm ⋮ Kadec-Klee properties of Calderón-Lozanovskiĭ function spaces ⋮ Locally uniform convexity in Musielak-Orlicz function spaces of Bochner type endowed with the Luxemburg norm ⋮ Nearly strict convexity in Musielak-Orlicz-Bochner function spaces ⋮ On some geometric properties of generalized Orlicz-Lorentz function spaces ⋮ The Banach-Saks properties in Orlicz-Lorentz spaces ⋮ Some fundamental geometric and topological properties of generalized Orlicz-Lorentz function spaces ⋮ Monotonicity Properties of Banach Lattices and Their Applications – a Survey ⋮ Lower and upper local uniform \(K\)-monotonicity in symmetric spaces ⋮ Kadec-Klee properties of Calderón-Lozanovskiĭ sequence spaces ⋮ Local rotundity structure of generalized Orlicz-Lorentz sequence spaces ⋮ Local monotonicity structure of symmetric spaces with applications ⋮ Rotundity structure of local nature for generalized Orlicz-Lorentz function spaces ⋮ Property \(\beta \) of Rolewicz and orthogonal convexities of Calderón-Lozanovski spaces ⋮ Local approach to Kadec-Klee properties in symmetric function spaces ⋮ Order asymptotically isometric copies of \(l^{\infty}\), \(l^{1}\) and \(c_{0}\) in Banach function spaces ⋮ Approximative compactness and full rotundity in Musielak--Orlicz spaces and Lorentz--Orlicz spaces ⋮ Kadec-Klee properties of some quasi-Banach function spaces ⋮ Moduli and characteristics of monotonicity in general Banach lattices and in Orlicz spaces in particular ⋮ Kadec-Klee properties of Orlicz-Lorentz sequence spaces equipped with the Orlicz norm ⋮ Isomorphic copies in the lattice \(E\) and its symmetrization \(E^{(*)}\) with applications to Orlicz-Lorentz spaces ⋮ Rotundity and uniform rotundity of Orlicz-Lorentz sequence spaces equipped with the Orlicz norm ⋮ Problems of existence of order copies of \(\ell ^\infty\) and \(L_p(\nu )\) in some non-Banach Köthe spaces ⋮ Symmetric spaces of measurable functions: some new and old advances ⋮ On geometric structure of symmetric spaces

This page was built for publication: Geometric properties of symmetric spaces with applications to Orlicz-Lorentz spaces