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Év szerint | Hónap szerint | Ugrás a hónaphoz | |
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Ábel Komálovics (BME): A one parameter extension of the Bures and Hellinger distances, and trace characterisations |
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Kedd, 8. November 2022, 11:00 - 12:00
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We study a one parameter extension of the Bures and Hellinger distances. It is the square root of the trace of the difference of the arithmetic mean and a sort of geometric mean. We characterize the parameters for which the extension is a true metric on the pure states of a Hilbert space. After this, we examine whether the extension is well-defined in the far more general C*-algebraic context. We present two statements concerning the order between the arithmetic mean and the variants of the geometric mean appearing in the extension in question. One of them characterises the central elements of a C*-algebra, the other one characterises the traciality of positive linear functionals. Our last statement characterises the tracial self-adjoint linear functionals of a von Neumann algebra which, in the finite dimensional case, can also be viewed as a characterisation of the determinant.
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