All Questions

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 ...

Let $E$ be a real normed space, and let $v_1,...,v_n\in E$ be linearly independent. The parallelepiped defined by these vectors is $P=\{\sum_{i=1}^{n}\alpha_i v_i|~0\le\alpha_i\le 1\}$. Since $E$ is a ...

Take $p\in (1,\infty)\setminus \{2\}$. Let $X$ be a subspace of $\ell_p^n$ and let $U\colon X\to \ell_p^m$ ($m\geqslant n$) be a linear isometry. Is it possible to extend $U$ to a (non-surjective) ...