Work

Isometric copies of ℓ_{∞}ⁿ in Lipschitz-free spaces over finite metric spaces

Year: 2026

Type: article

Abstract: For every $n\in\mathbb N$, we construct a finite metric subspace $M_n$ of $\ell_\infty^n$ such that the Lipschitz-free space $\mathcal F(M_n)$ contains a linear isometric copy of $\ell_\infty^n$. This answers a question posed by Khan, Mim, and Ostrovskii, who obtained examples in dimensions three and four. As a consequence, the finite-dimensional real Banach spaces that admit a linear isometric embedding into a Lipschitz-free space over a finite metric space are precisely the polyhedral spaces.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17960

Author: Rainis Haller

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Eesti Teadusagentuur

Award: Plasticity and extremal geometric structure of the unit ball of Banach spaces with applications to the study of Lipschitz spaces, vector-valued functions spaces and tensor products

OpenAlex ID: W7223202729

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