TRACE INEQUALITIES AND QUANTUM ENTROPY: An introductory course

We give an elementary introduction to the subject of trace inequalities and related topics in analysis, with a special focus on results that are relevant to quantum statistical mechanics. This is a preliminary draft prepared for participants in Entropy and the Quantum: A school on analytic and functional inequalities with applications, Tucson, Arizona, March 16-20, 2009. Mathematics subject classification numbers: 47A63, 15A90

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