Extending surjective isometries defined on the unit sphere of ℓ_∞(Γ)

2017/09/27 by Antonio M. Peralta, Peralta, Antonio M.
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results

paper · pdf · doi:10.48550/arxiv.1709.09584

openalex publication_date 2017/09/27 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28

Abstract

Let Γ be an infinite set equipped with the discrete topology. We prove that the space ℓ_∞(Γ), of all complex-valued bounded functions on Γ, satisfies the Mazur-Ulam property, that is, every surjective isometry from the unit sphere of ℓ_∞(Γ) onto the unit sphere of an arbitrary complex Banach space X admits a unique extension to a surjective real linear isometry from ℓ_∞(Γ) to X.

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