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Banach space

Uniformly convex Banach space

{c}
{wiki=Clarkson's_inequalities}

For $2\leq p<\infty$, the Clarkson inequality is
$$
\left\lVert\frac{f+g}{2}\right\rVert_p^p
+\left\lVert\frac{f-g}{2}\right\rVert_p^p
\leq\frac{\lVert f\rVert_p^p+\lVert g\rVert_p^p}{2}.
$$
It gives the uniform convexity of $L^p$.

= Banach spaces
{c}
{synonym}

Clarkson inequality

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 106 / 2 / b / Solution

codex/banach-spaces

Clarkson inequality

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Clarkson inequality

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