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Sharp uniform convexity and smoothness inequalities for trace norms. (English) Zbl 0803.47037
Summary: We prove several sharp inequalities specifying the uniform convexity and uniform smoothness properties of the Schatten trace ideals $C\sb p$, which are the analogs of the Lebesgue spaces $L\sb p$ in non-commutative integration. The inequalities are all precise analogs of results which had been known in $L\sb p$, but were only known in $C\sb p$ for special values of $p$. In the course of our treatment of uniform convexity and smoothness inequalities for $C\sb p$ we obtain new and simple proofs of the known inequalities for $L\sb p$.

47L20Operator ideals
46B20Geometry and structure of normed linear spaces
46L51Noncommutative measure and integration
46L53Noncommutative probability and statistics
46L54Free probability and free operator algebras
Full Text: DOI EuDML
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