There is no finitely isometric Krivine's theorem

James Kilbane; Mikhail I. Ostrovskii

There is no finitely isometric Krivine's theorem

Functional Analysis 2018-11-13 v1 Metric Geometry

Authors: James Kilbane , Mikhail I. Ostrovskii

Abstract

We prove that for every $p\in(1,\infty)$ , $p\ne 2$ , there exist a Banach space $X$ isomorphic to $\ell_p$ and a finite subset $U$ in $\ell_p$ , such that $U$ is not isometric to a subset of $X$ . This result shows that the finite isometric version of the Krivine theorem (which would be a strengthening of the Krivine theorem (1976)) does not hold.

Keywords

Krivine's theorem finite isometric version Banach space ℓ_p space isometry

Cite

@article{arxiv.1708.01570,
  title  = {There is no finitely isometric Krivine's theorem},
  author = {James Kilbane and Mikhail I. Ostrovskii},
  journal= {arXiv preprint arXiv:1708.01570},
  year   = {2018}
}

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