Abstract
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.
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Uchiyama, M., Hasumi, M. On some operator monotone functions. Integr equ oper theory 42, 243–251 (2002). https://doi.org/10.1007/BF01275518
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DOI: https://doi.org/10.1007/BF01275518