The Mazur-Ulam property for the space of complex null sequences

2017/08/28 by Jiménez-Vargas, Antonio, Campoy, Antonio Morales, Peralta, Antonio M. +1
#FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1708.08538

Abstract

Given an infinite set Γ, we prove that the space of complex null sequences c₀(Γ) satisfies the Mazur-Ulam property, that is, for each Banach space X, every surjective isometry from the unit sphere of c₀(Γ) onto the unit sphere of X admits a (unique) extension to a surjective real linear isometry from c₀(Γ) to X. We also prove that the same conclusion holds for the finite dimensional space ℓ_∞^m.

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