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