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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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up vote 0 down vote accepted

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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Matrix Analysis by Rajendra Bhatia

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Does this cover infinite dimensions? (The notion of "trace class" is trivial in finite dimensions) –  Normal Human Jul 15 at 19:53
I donot remember it, but The Homology of Banach and Topological Algebras by A. Ya. Helemskii will be helpful for you. –  Razieh Noori Jul 15 at 20:18

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