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Let $H$ be a separable Hilbert space. What is the closure of the set of Hilbert-Schmidt operators on $H$ in the set of bounded, linear operators on $H$ with respect to the strong operator topology? A reference would be muchly appreciated.

Best, Luke

  • I found the answer here: https://math.stackexchange.com/questions/269972/bounded-operators-on-separable-hilbert-spaces – Peter Wacken Mar 18 '20 at 17:00

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