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This is a follow-up to this question of mine. It is well-known that the Banach space $\ell_1$ does not contain any isomorphic copies of $c_0$. One can even go further and show that $\ell_1$ does not ...

The goal of this question is to develop further the discussion initiated in Under which conditions is it possible to find points with same distances under bi-Lipschitz map. The mentioned question was ...

Let $Y$ be a Banach space isomorphic to $\ell_p$, $1<p<\infty$. Is it true that any finite subset of $\ell_p$ is isometric to some finite subset of $Y$? It seems to me that it is an interesting ...