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Elementary Proof of Petz–Hasegawa Theorem

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We give an elementary proof of the following important result first stated by Petz–Hasegawa:

$$\begin{array}{ll}f_{p}(t)= p (1-p) \frac{(t-1)^2}{(t^{p}-1) (t^{1-p}-1)}\; {\rm is\; an\; operator\; monotone\; function\; for }\; -1 \le p \le 2\end{array}$$


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Correspondence to Takayuki Furuta.

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To the memory of Professor Tsuneo Kanno who passed away by tsunami disaster at Tohoku district on 2011.3.11 with deep sorrow

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Furuta, T. Elementary Proof of Petz–Hasegawa Theorem. Lett Math Phys 101, 355–359 (2012).

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