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1. Given $p\in (1,\infty)$.

2. Let us fix two, non-isometric subspaces $X,Y\subseteq \ell_p$ isomorphic to $\ell_p$.

3. Are there an $\varepsilon\in (0,1)$ and an operator $S\colon X\to Y$ such that

$$(1-\varepsilon)\|x\|\leqslant \|Sx\|\leqslant (1+\varepsilon)\|x\|$$

holds for each $x\in X$?

1. Given $p\in (1,\infty)$.

2. Let us fix two, non-isometric subspaces $X,Y\subseteq \ell_p$ isomorphic to $\ell_p$.

3. Are there an $\varepsilon\in (0,1)$ and an isomorphism $S\colon X\to Y$ such that

$$(1-\varepsilon)\|x\|\leqslant \|Sx\|\leqslant (1+\varepsilon)\|x\|$$

holds for each $x\in X$?

1. Given $p\in (1,\infty)$.

2. Let us fix two, non-isometric subspaces $X,Y\subseteq \ell_p$ isomorphic to $\ell_p$.

3. Are there an $\varepsilon\in (0,1)$ and an operator $S\colon X\to Y$ such that

$$(1-\varepsilon)\|x\|\leqslant \|Sx\|\leqslant (1+\varepsilon)\|x\|$$

holds for each $x\in X$?

1. Given $p\in (1,\infty)$.

2. Let us fix two, non-isometric subspaces $X,Y\subseteq \ell_p$ isomorphic to $\ell_p$.

3. Are there an $\varepsilon\in (0,1)$ and an operator $S\colon X\to Y$ such that

$$(1-\varepsilon)\|x\|\leqslant \|Sx\|\leqslant (1+\varepsilon)\|x\|$$

holds for each $x\in X$?

1. Given $p\in (1,\infty)$.

2. Let us fix two subspaces $X,Y\subseteq \ell_p$ isomorphic to $\ell_p$.

3. Are there an $\varepsilon\geqslant0$ and an operator $S\colon X\to Y$ such that

$$(1-\varepsilon)\|x\|\leqslant \|Sx\|\leqslant (1+\varepsilon)\|x\|$$

holds for each $x\in X$?

1. Given $p\in (1,\infty)$.

2. Let us fix two, non-isometric subspaces $X,Y\subseteq \ell_p$ isomorphic to $\ell_p$.

3. Are there an $\varepsilon\in (0,1)$ and an operator $S\colon X\to Y$ such that

$$(1-\varepsilon)\|x\|\leqslant \|Sx\|\leqslant (1+\varepsilon)\|x\|$$

holds for each $x\in X$?