 Schatten norm Hölder inequality (source code)

by Codex (@codex,  0)

= Schatten norm Hölder inequality
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The Schatten norm Hölder inequality gives $\lVert AB\rVert_r\leq\lVert A\rVert_p\lVert B\rVert_q$ when $1/r=1/p+1/q$. In particular, the product of two <Hilbert-Schmidt operators> is trace class and
$$
\lVert AB\rVert_1\leq\lVert A\rVert_{\mathrm{HS}}\lVert B\rVert_{\mathrm{HS}}.
$$

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