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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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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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  • $\begingroup$ Does this cover infinite dimensions? (The notion of "trace class" is trivial in finite dimensions) $\endgroup$ – user147263 Jul 15 '15 at 19:53
  • $\begingroup$ I donot remember it, but The Homology of Banach and Topological Algebras by A. Ya. Helemskii will be helpful for you. $\endgroup$ – R.N Jul 15 '15 at 20:18

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