SHARP UNIFORM CONVEXITY AND SMOOTHNESS INEQUALITIES FOR TRACE NORMS

We prove several sharp inequalities specifying the uniform convexity and uniform smoothness properties of the Schatten trace ideals C(p), which are the analogs of the Lebesgue spaces L(p) in non-commutative integration. The inequalities are all precise analogs of results which had been known in L(p), but were only known in C(p) for special values of p. In the course of our treatment of uniform convexity and smoothness inequalities for C(p) we obtain new and simple proofs of the known inequalities for L(p).