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What is the motivation for trace class operators? Can anybody suggest the most general and standard reference that includes Schatten $p$ class operators as well? I have the following references.

  1. Operator theory by Conway
  2. Operator theory in function spaces by Kehe Zhu

Can anybody suggest even better?

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Also seen at mathoverflow.net/questions/150915/… –  anon Dec 5 '13 at 18:40

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See Trace Ideals and Their Applications by Barry Simon. He covers the general theory of Schatten ideals and their applications, with particular attention to applications in quantum physics.

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