Isometric embedding of ℓ₁ into Lipschitz-free spaces and ℓ_{∞} into their duals

DOI10.1090/proc/13590zbMath1388.46012arXiv1604.04131OpenAlexW3122529198MaRDI QIDQ5270142

Marek Cúth, Michal Johanis

Publication date: 22 June 2017

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.04131

zbMATH Keywords

Lipschitz-free spacesrotundisometric embedding of \(\ell_\infty\)isometric embedding of \(\ell_1\)

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Isomorphic theory (including renorming) of Banach spaces (46B03) Isometric theory of Banach spaces (46B04)

Related Items (11)

Norm-attaining lattice homomorphisms ⋮ A characterisation of octahedrality in Lipschitz-free spaces ⋮ Complementability of isometric copies of \(\ell_1\) in transportation cost 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 ⋮ A pre-adjoint approach on weighted composition operators between spaces of Lipschitz functions ⋮ On relations between transportation cost spaces and \(\ell_1\) ⋮ Embeddability of \(\ell_p\) and bases in Lipschitz free \(p\)-spaces for \(0 < p \leq 1\) ⋮ Generalized transportation cost spaces ⋮ Isometric structure of transportation cost spaces on finite metric spaces ⋮ Closed linear spaces consisting of strongly norm attaining Lipschitz functionals

Cites Work

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• Isometric copies of \(c_0\) and \(\ell^{\infty}\) in duals of Banach spaces
• Banach space theory. The basis for linear and nonlinear analysis
• On the structure of Lipschitz-free spaces
• Remarks on James's distortion theorems II
• Lipschitz-free Banach spaces
• On complemented versions of James’s distortion theorems
• Biorthogonal systems in Banach spaces

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