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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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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