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) linear isometry $ \hat{U}\colon \ell_p^n\to \ell_p^m$ ? For contractions this is not necessarily true however theRead more
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