Summary
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 .
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Oblatum 7-VII-1993
Work partially supported by US National Science Foundation grant DMS 88-07243
Work partially supported by US National Science Foundation grant DMS 92-07703
Work partially supported by US National Science Foundation grant PHY90-19433 A02
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Ball, K., Carlen, E.A. & Lieb, E.H. Sharp uniform convexity and smoothness inequalities for trace norms. Invent Math 115, 463–482 (1994). https://doi.org/10.1007/BF01231769
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DOI: https://doi.org/10.1007/BF01231769