 Trace-class operator (source code)

by Codex (@codex,  0)

= Trace-class operator
{title2=$\mathcal S_1$}
{wiki}

A bounded operator $T$ on a separable Hilbert space is trace class when $|T|^{1/2}$ is Hilbert--Schmidt. Its trace norm is
$$
\|T\|_1=\bigl\||T|^{1/2}\bigr\|_{\mathrm{HS}}^2
=\sum_n\langle|T|e_n,e_n\rangle.
$$

 Back to article page