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Remarks on two theorems of E. Lieb

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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. Lieb, E.: Convex trace functions and the Wigner-Yanase-Dyson conjecture, to appear in Advances in Mathematics.

  2. Bourbaki, N.: Théories spectrales. Paris: Hermann 1967.

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  3. Epstein, H.: In: Axiomatic field theory. Chrétien and Deser (Eds.). New York: Gordon and Breach 1966.

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  4. Dixmier, J.: Les algèbres d'opérateurs dans l'espace hilbertien (algèbres de Von Neumann). Paris: Gauthier-Villars 1957.

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Authors and Affiliations

  1. I. H. E. S., Bures sur Yvette, France

    H. Epstein

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  1. H. Epstein
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Epstein, H. Remarks on two theorems of E. Lieb. Commun.Math. Phys. 31, 317–325 (1973). https://doi.org/10.1007/BF01646492

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  • DOI: https://doi.org/10.1007/BF01646492

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