On embeddings of finite subsets of ℓ₂

2016/09/28 by Kilbane, James
#FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1609.08971

Abstract

We study finite subsets of ℓ₂, and more generally any metric space, and consider whether these isometrically embed into a Banach space. Our results partially answer a question of Ostrovskii, on whether every infinite-dimensional Banach space contains every finite subset of ℓ₂ isometrically. The updated version contains acknowledgement that Theorem 3.1 has been proven previously in a paper of Shkarin.

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