Sharp uniform convexity and smoothness inequalities for trace norms

Keith Ball; Eric A. Carlen; Elliott H. Lieb

doi:10.1007/BF01231769

Sharp uniform convexity and smoothness inequalities for trace norms

Keith Ball, Eric A. Carlen, Elliott H. Lieb

Mathematics

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250 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	463-482
Number of pages	20
Journal	Inventiones Mathematicae
Volume	115
Issue number	1
DOIs	https://doi.org/10.1007/BF01231769
State	Published - Dec 1994

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/BF01231769

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

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AU - Lieb, Elliott H.

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Sharp uniform convexity and smoothness inequalities for trace norms

Abstract

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