Schatten class

Summary

For $1 \le p < \infty$, the Schatten $p$-class consists of the compact operators on a Hilbert space whose sequence of singular values is $p$-summable. These classes are the operator analogues of the sequence spaces $\ell^p$. The case $p = 1$ is the trace class and the case $p = 2$ is the Hilbert–Schmidt class, the two most used ideals of operators.