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A Hilbert space $H$ is a real or complex vector space endowed with an inner product such that $H$ is a complete metric space when endowed with the norm induced by this inner product.

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Compactness in trace class operators space

The space of trace class operators is nothing but $\ell^2\hat{\otimes}\ell^2$. There is a result by Grothendieck, see e.g. the snippet from [DiestelPuglisi2009].
Onur Oktay's user avatar
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