{title2=$\lVert T\rVert_{\mathrm{HS}}$}
{wiki=Hilbert–Schmidt_operator}

An operator on a Hilbert space is Hilbert--Schmidt when
$$
\lVert T\rVert_{\mathrm{HS}}^2=\sum_n\lVert Te_n\rVert^2<\infty
$$
for one, equivalently every, Hilbertian basis. Every Hilbert--Schmidt operator is compact.


Hilbert-Schmidt operator

{wiki=Hilbert–Schmidt_operator}

A Hilbert–Schmidt operator is a special type of compact linear operator acting on a Hilbert space, which can be characterized by certain properties of its kernel. Specifically, it is defined in the context of an inner product space, typically \$L^2\$ spaces.


 Hilbert–Schmidt operator

ID: hilbert-schmidt-operator