Schatten norm

In mathematics, specifically functional analysis, the Schatten norm (or Schatten–von-Neumann norm) arises as a generalization of p-integrability similar to the trace class norm and the Hilbert–Schmidt norm.

Let ${\displaystyle H_{1}}$, ${\displaystyle H_{2}}$ be separable Hilbert spaces, and ${\displaystyle T}$ a (linear) bounded operator from ${\displaystyle H_{1}}$ to ${\displaystyle H_{2}}$. For ${\displaystyle p\in [1,\infty )}$, define the Schatten p-norm of ${\displaystyle T}$ as

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