$r$-separated sequence in Hilbert spaces

Asked Jan 07 '18 at 16:57

Active Jan 07 '18 at 16:57

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I'm trying (with no good results) to prove the follwing:

Prop. Let $B^1\subset H$ be the unit ball in the Hilbert space $H$. If $(x_n)_{n\in\mathbb{N}}\subset B^1$ is a $r$-separated sequence, i.e. $\vert\vert x_j-x_k\vert\vert\geq r$, for any $j\neq k$, then $r\leq \sqrt{2}$.

Can you help me to prove the reult above?

asked Jan 07 '18 at 16:57

Vincenzo Zaccaro

3,210

What bad results do you have? We need to see some sort of attempt/// – mathworker21 Jan 07 '18 at 17:00
Many thanks. I think we can close the question. – Vincenzo Zaccaro Jan 07 '18 at 17:28

$r$-separated sequence in Hilbert spaces

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