Communications in Mathematical Physics

, Volume 31, Issue 4, pp 317–325 | Cite as

Remarks on two theorems of E. Lieb

  • H. Epstein
Article

Abstract

The concavity of two functions of a positive matrixA, Tr exp(B + logA) and TrA r KA p K* (whereB=B* andK are fixed matrices), recently proved by Lieb, can also be obtained by using the theory of Herglotz functions.

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References

  1. 1.
    Lieb, E.: Convex trace functions and the Wigner-Yanase-Dyson conjecture, to appear in Advances in Mathematics.Google Scholar
  2. 2.
    Bourbaki, N.: Théories spectrales. Paris: Hermann 1967.Google Scholar
  3. 3.
    Epstein, H.: In: Axiomatic field theory. Chrétien and Deser (Eds.). New York: Gordon and Breach 1966.Google Scholar
  4. 4.
    Dixmier, J.: Les algèbres d'opérateurs dans l'espace hilbertien (algèbres de Von Neumann). Paris: Gauthier-Villars 1957.Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • H. Epstein
    • 1
  1. 1.I. H. E. S.Bures sur YvetteFrance

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