Inventiones mathematicae

, Volume 115, Issue 1, pp 463–482 | Cite as

Sharp uniform convexity and smoothness inequalities for trace norms

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


We prove several sharp inequalities specifying the uniform convexity and uniform smoothness properties of the Schatten trace idealsC p , which are the analogs of the Lebesgue spacesL p in non-commutative integration. The inequalities are all precise analogs of results which had been known inL p , but were only known inC p for special values ofp. In the course of our treatment of uniform convexity and smoothness inequalities forC p we obtain new and simple proofs of the known inequalities forL p .


Simple Proof Trace Norm Uniform Convexity Smoothness Property Sharp Inequality 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Keith Ball
    • 1
  • Eric A. Carlen
    • 2
  • Elliott H. Lieb
    • 3
  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA
  2. 2.Georgia Institute of TechnologySchool of MathematicsAtlantaUSA
  3. 3.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonUSA

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