6 ehhh

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 operatorisomorphism $S\colon X\to Y$ such that

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

holds for each $x\in X$?

5 dr

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 $x\in X$?

4 dr

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 $\varepsilon\geqslant0$ \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\$?

3 clar
2 dr
1