Non-squareness properties of Orlicz spaces equipped with the \(p\)-Amemiya norm

DOI10.1016/J.NA.2012.02.014zbMath1247.46015OpenAlexW2073097842MaRDI QIDQ417763

Karol Wlaźlak, Henryk Hudzik, Marek Wisła, Yun An Cui

Publication date: 14 May 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2012.02.014

zbMATH Keywords

Orlicz spaceconvergence in measureuniform non-squarenessnon-squareness\(p\)-Amemiya normlinearly isometric spaceslinearly isomorphic spaceslocally uniformly non-squareness

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) Geometry and structure of normed linear spaces (46B20)

Related Items (17)

Uniformly non-square points and representation of functionals of Orlicz-Bochner sequence spaces ⋮ On a certain class of norms in semimodular spaces and their monotonicity properties ⋮ The fixed point property of Orlicz sequence spaces equipped with the \(p\)-Amemiya norm ⋮ Uniform nonsquareness and locally uniform nonsquareness in Orlicz-Bochner function spaces and applications ⋮ Exposed points of Orlicz function spaces equipped with \(p\)-Amemiya norms ⋮ Smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with \(p\)-Amemiya norms ⋮ Some remarks on the geometry of Lorentz spaces ⋮ Packing constant in Orlicz sequence spaces equipped with the \(p\)-Amemiya norm ⋮ Uniform rotundity in every direction of Orlicz function spaces equipped with the \(p\)-Amemiya norm ⋮ Monotonicity properties and dominated best approximation problems in Orlicz spaces equipped with the \(p\)-Amemiya norm ⋮ Monotonicity properties and solvability of dominated best approximation problem in Orlicz spaces equipped with $s$-norms ⋮ \(M\)-constants, Dominguez-Benavides coefficient, and weak fixed point property in Orlicz sequence spaces equipped with the \(p\)-Amemiya norm ⋮ Smoothness of Orlicz function spaces equipped with the \(p\)-Amemiya norm ⋮ Orlicz spaces equipped with \(s\)-norms ⋮ Geometry of Orlicz spaces equipped with norms generated by some lattice norms in \(\mathbb{R}^{2}\) ⋮ Exposed points of Orlicz sequence spaces equipped with \(p\)-Amemiya \((1\leq p\leq \infty)\) norms ⋮ Strict convexity of Orlicz sequence spaces equipped with \(p\)-Amemiya norms

Cites Work

• Orlicz spaces and modular spaces
• Basic theory of \(p\)-Amemiya norm in Orlicz spaces (\(1\leq p\leq \infty\)): Extreme points and rotundity in Orlicz spaces endowed with these norms
• Strongly extreme points in Orlicz spaces equipped with the \(p\)-Amemiya norm
• On the convexity coefficient of Orlicz spaces
• Uniformly non-\(\ell^{(1)}_n\) Musielak-Orlicz sequence spaces
• Characteristic of convexity of Köthe function spaces
• von Neumann-Jordan constant and uniformly non-square Banach spaces
• Uniformly non-square Banach spaces
• Uniformly nonsquare Banach spaces have the fixed point property for nonexpansive mappings
• Uniformly non-\(l_ n^{(1)}\) Orlicz spaces
• On James and Jordan–von Neumann constants and the normal structure coefficient of Banach spaces
• Skewness in Banach Spaces
• Uniformly non-$l_{n}^{(1)}$ Orlicz spaces with Luxemburg norm
• Uniform non-squareness of ψ-direct sums of Banach spaces X ⊕_ψ Y
• On James and Jordan-von Neumann constants of Lorentz sequence spaces
• Amemiya norm equals Orlicz norm in general
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Non-squareness properties of Orlicz spaces equipped with the \(p\)-Amemiya norm