Let $X$ be a Hilbert space containing functions defined over a bounded region $\Omega\subset \mathbb{R}^N$. Assume $f_n\in X$ converges weakly to $f\in X$, and also has a strongly convergent subsequence, say $f_{n_k}$, converging to $f$. Can we say that $f_n\to f$ strongly?

## **closed** as off-topic by Ben McKay, Jan-Christoph Schlage-Puchta, András Bátkai, Ilya Bogdanov, Sean Eberhard Oct 21 at 10:04

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