Let $1<p,q<\infty$, so I need to find a norm of identity operator $J: l^n_p \to l^n_q$
When $p\le q$, it's quite easy for me to understand that $||J||=1$ (beacuse in this case $||x||_q \le ||x||_p$, so $\frac{||x||_q}{||x||_p} \le 1$ and it's easy to find vector on which $\frac{||x||_q}{||x||_p} = 1$ )
But when $p > q$, things get trickier. So I have a hypotesis that the answer in this case is $\frac{n^{1/q}}{n^{1/p}}$ and I had some approach to prove it but I couldn't finish it