Hilbert-Schmidt operator
= Hilbert-Schmidt operator
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{title2=$T\in\mathcal S_2$}
{wiki=Hilbert–Schmidt_operator}
= Hilbert-Schmidt
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A bounded <linear operator> on a <Hilbert space> is Hilbert-Schmidt when $\sum_n\|Te_n\|^2<\infty$ for one, equivalently every, <orthonormal basis>. Every Hilbert-Schmidt operator is a <compact operator>.