Norm-attaining Lipschitz functionals

DOI10.1215/17358787-3639646zbMath1358.46009arXiv1601.07821OpenAlexW2517686101MaRDI QIDQ307021

Mariia Soloviova, Miguel Martín, Vladimir Kadets

Publication date: 1 September 2016

Published in: Banach Journal of Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.07821

zbMATH Keywords

uniformly convex Banach spacesBishop-Phelps-Bollobás property (BPBp)Lipschitz free spaceLipschitz functionalsnorm attaining functionals

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Isometric theory of Banach spaces (46B04) Radon-Nikodým, Kre?n-Milman and related properties (46B22) Nonlinear classification of Banach spaces; nonlinear quotients (46B80)

Related Items (20)

The Bishop–Phelps–Bollobás Theorem: An Overview ⋮ Extremal structure and duality of Lipschitz free spaces ⋮ NORMAL FUNCTIONALS ON LIPSCHITZ SPACES ARE WEAK^* CONTINUOUS ⋮ Some stability properties for the Bishop–Phelps–Bollobás property for Lipschitz maps ⋮ Cantor sets of low density and Lipschitz functions on \(C^1\) curves ⋮ Norm attaining operators and variational principle ⋮ Octahedral norms in duals and biduals of Lipschitz-free spaces ⋮ Points of differentiability of the norm in Lipschitz-free spaces ⋮ Some results on isometric composition operators on Lipschitz spaces ⋮ Several remarks on norm attainment in tensor product spaces ⋮ On isometric embeddings into the set of strongly norm-attaining Lipschitz functions ⋮ Infinite dimensional spaces in the set of strongly norm-attaining Lipschitz maps ⋮ Emerging notions of norm attainment for Lipschitz maps between Banach spaces ⋮ Examples and applications of the density of strongly norm attaining Lipschitz maps ⋮ On strongly norm attaining Lipschitz maps ⋮ Norm-attaining tensors and nuclear operators ⋮ Closed linear spaces consisting of strongly norm attaining Lipschitz functionals ⋮ The Bishop-Phelps-Bollobás property for Lipschitz maps ⋮ Residuality in the set of norm attaining operators between Banach spaces ⋮ Norm attaining Lipschitz maps toward vectors

Cites Work

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• On embedding uniform and topological spaces
• The Bishop-Phelps-Bollobás theorem for operators
• Optimization of functions on certain subsets of Banach spaces
• Bishop-Phelps-Bollobás moduli of a Banach space
• The Bishop-Phelps-Bollobás Theorem for bilinear forms
• A proof that every Banach space is subreflexive
• The Daugavet property for spaces of Lipschitz functions
• Lipschitz-free Banach spaces
• An Extension to the Theorem of Bishop and Phelps

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