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Sharp uniform convexity and smoothness inequalities for trace norms

In: Inequalities

Author

Listed:
  • 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)

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.

Suggested Citation

  • Keith Ball & Eric A. Carlen & Elliott H. Lieb, 2002. "Sharp uniform convexity and smoothness inequalities for trace norms," Springer Books, in: Michael Loss & Mary Beth Ruskai (ed.), Inequalities, pages 171-190, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55925-9_18
    DOI: 10.1007/978-3-642-55925-9_18
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