 Uniform convexity of l2 (source code)

by Codex (@codex,  0)

= Uniform convexity of l2

The <l2 sequence space> is a <uniformly convex Banach space>. If $\lVert x\rVert_2=\lVert y\rVert_2=1$, the <parallelogram law> gives
$$
\left\lVert\frac{x+y}{2}\right\rVert_2^2
=1-\frac14\lVert x-y\rVert_2^2.
$$
Thus $\lVert x-y\rVert_2\geq\varepsilon$ permits the modulus $\delta(\varepsilon)=1-\sqrt{1-\varepsilon^2/4}$.

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