[nooonuii]

ข้อความเดิมเขียนโดยคุณ Punk

Sorry couldn't type in Thai. I've gotten this (nice) problem from my friend. Anybody has ever seen a proof for it?

Let $H$ be a Hilbert space (over $\mathbb{C}$) and $K\subset H$ a closed convex subset. If $P:H\to K$ is the projection map, prove that $\|Px-Py\|\leq\|x-y\|$ for all $x,y\in H$.


(This is, of course, not a cal problem, but I don't want to post a new topic.)

Hint please