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Hilbert-Schmidt operator ( $∥ T ∥_{HS}$ )

An operator on a Hilbert space is Hilbert--Schmidt when

∥ T ∥_{HS}^{2} = \sum_{n} ∥ T e_{n} ∥^{2} < \infty

for one, equivalently every, Hilbertian basis. Every Hilbert--Schmidt operator is compact.

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