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arXiv · 1708.01570

There is no finitely isometric Krivine's theorem

James Kilbane·Mikhail I. Ostrovskii
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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.

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James Kilbane, Mikhail I. Ostrovskii. 2017-08-04. There is no finitely isometric Krivine's theorem. https://arxiv.org/abs/1708.01570

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