# Sharp uniform convexity and smoothness inequalities for trace norms

@article{Ball1994SharpUC, title={Sharp uniform convexity and smoothness inequalities for trace norms}, author={Keith Ball and Eric A. Carlen and Elliott H. Lieb}, journal={Inventiones mathematicae}, year={1994}, volume={115}, pages={463-482} }

SummaryWe prove several sharp inequalities specifying the uniform convexity and uniform smoothness properties of the Schatten trace idealsCp, which are the analogs of the Lebesgue spacesLp in non-commutative integration. The inequalities are all precise analogs of results which had been known inLp, but were only known inCp for special values ofp. In the course of our treatment of uniform convexity and smoothness inequalities forCp we obtain new and simple proofs of the known inequalities forLp.

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