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MR1002123 (90h:47032) 47A60 (47B15)
Furuta, Takayuki $A\ge B\ge 0$ ensures $B\sp rA\sp pB\sp r\ge(B\sp rA\sp {p-s}B\sp r)\sp {(p+2r)/(p-s+2r)}$ for $1\ge 2r\ge 0,\;p\ge s\ge 0$ with $p+2r\ge 2s$. J. Operator Theory 21 (1989), no. 1, 107--115.
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