Sharp uniform convexity and smoothness inequalities for trace norms

Keith Ball, Eric A. Carlen and Elliott H. Lieb
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Keith Ball: Texas A&M University, Department of Mathematics
Eric A. Carlen: Georgia Institute of Technology, School of Mathematics
Elliott H. Lieb: Princeton University, Departments of Mathematics and Physics

A chapter in Inequalities, 2002, pp 171-190 from Springer

Abstract: Summary 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.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55925-9_18

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DOI: 10.1007/978-3-642-55925-9_18

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