Equivalent norms with the property \((\beta)\) of Rolewicz

DOI10.1007/s13398-016-0278-2zbMath1432.46002arXiv1506.07978OpenAlexW806284855MaRDI QIDQ506260

Yong-Cai Geng, Sumit K. Garg

Publication date: 31 January 2017

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.07978

zbMATH Keywords

convexitynon-separable Banach spacesasymptotic uniform smoothnessproperty $(\beta)$renormings

Mathematics Subject Classification ID

Isomorphic theory (including renorming) of Banach spaces (46B03) Nonseparable Banach spaces (46B26) Nonlinear classification of Banach spaces; nonlinear quotients (46B80) Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science (46B85) Asymptotic theory of Banach spaces (46B06)

Related Items (17)

Power type asymptotically uniformly smooth and asymptotically uniformly flat norms ⋮ Asymptotic geometry and Delta-points ⋮ On the geometry of the countably branching diamond graphs ⋮ A submetric characterization of Rolewicz’s property $(\beta )$ ⋮ On Kalton’s interlaced graphs and nonlinear embeddings into dual Banach spaces ⋮ Universality, complexity and asymptotically uniformly smooth Banach spaces ⋮ On strong asymptotic uniform smoothness and convexity ⋮ Umbel convexity and the geometry of trees ⋮ \(\xi\)-asymptotically uniformly smooth, \(\xi\)-asymptotically uniformly convex, and (\(\beta\)) operators ⋮ Power type \(\xi\)-asymptotically uniformly smooth and \(\xi\)-asymptotically uniformly flat norms ⋮ Asymptotic properties of Banach spaces and coarse quotient maps ⋮ (β)-distortion of some infinite graphs ⋮ On the weak maximizing properties ⋮ On the Coarse Geometry of James Spaces ⋮ On the embeddability of the family of countably branching trees into quasi-reflexive Banach spaces ⋮ Prescribed Szlenk index of separable Banach spaces ⋮ Asymptotic smoothness in Banach spaces, three-space properties and applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The metrical interpretation of superreflexivity in Banach spaces
• \(k\)-\(\beta\) and \(k\)-nearly uniformly convex Banach spaces
• On asymptotic structure, the Szlenk index and UKK properties in Banach spaces
• Compactly uniformly convex spaces and property \((\beta)\) of Rolewicz
• Metrical characterization of super-reflexivity and linear type of Banach spaces
• Averaged norms
• Szlenk indices and uniform homeomorphisms
• The transfer of property $(\beta )$ of Rolewicz by a uniform quotient map
• ALMOST FRÉCHET DIFFERENTIABILITY OF LIPSCHITZ MAPPINGS BETWEEN INFINITE-DIMENSIONAL BANACH SPACES
• Asymptotic geometry of Banach spaces and uniform quotient maps
• On weak* uniformly Kadec-Klee renormings
• A new metric invariant for Banach spaces
• On ∆-uniform convexity and drop property
• Shorter Notes: A Short Proof of a Version of Asplund's Norm Averaging Theorem
• GEOMETRIC THEORY OF BANACH SPACES. PART II. GEOMETRY OF THE UNIT SPHERE

This page was built for publication: Equivalent norms with the property \((\beta)\) of Rolewicz