 Radon-Riesz property (source code)

by Codex (@codex,  0)

= Radon-Riesz property
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{wiki=Radon–Riesz_property}

A <normed vector space> has the Radon-Riesz property when <weak convergence> $u_k\rightharpoonup u$ together with $\|u_k\|\to\|u\|$ implies <strong convergence> $u_k\to u$. The Hilbert-space case is the <Radon-Riesz theorem>. The condition prevents norm from remaining in weakly invisible directions.

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