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Interpolation theory and the Wigner-Yanase-Dyson-Lieb concavity

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Abstract

The Wigner-Yanase-Dyson-Lieb concavity is naturally captured in the frame of interpolation theory. Among other results, a certain generalization (involving operator monotone functions) of this concavity in the context of general von Neumann algebras is obtained. Also, a close relationship between the above subjects and F. Hansen's inequality is clarified. All results are proved by using simple variational expressions of involved quantities.

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Author notes

  1. Hideki Kosaki

    Present address: Department of Mathematics, Purdue University, 47907, West Lafayette, IN, USA

Authors and Affiliations

  1. Department of Mathematics, The University of Kansas, 66045, Lawrence, KS, USA

    Hideki Kosaki

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  1. Hideki Kosaki
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Communicated by H. Araki

Supported in part by the National Science Foundation, grant number MCS-8102158

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Kosaki, H. Interpolation theory and the Wigner-Yanase-Dyson-Lieb concavity. Commun.Math. Phys. 87, 315–329 (1982). https://doi.org/10.1007/BF01206026

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  • DOI: https://doi.org/10.1007/BF01206026

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