, Volume 42, Issue 2, pp 243-251

On some operator monotone functions

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We try to find a continuous functionu defined on a real right half-line with the range (0, ∞) such thatu −1 is operator monotone. We then look for another functionv such thatv(u −1) is operator monotone, namely,u(A)≦u(B) impliesv(A)≦v(B) for self-adjoint operatorsA andB.