Abstract.
Let A,B be positive semidefinite matrices and \(|||\cdot|||\) any unitarily invariant norm on the space of matrices. We show \( |||f(A) + f(B)||| \geq |||f(A + B)|||\) for any non-negative operator monotone function f(t) on \([0,\infty)\), and \( |||g(A) + g(B)||| \leq |||g(A + B)||| \) for non-negative increasing function g(t) on \([0,\infty)\) with g(0) = 0 and \(g(\infty) = \infty\), whose inverse function is operator monotone.
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Received: 1 February 1999
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Ando, T., Zhan, X. Norm inequalities related to operator monotone functions. Math Ann 315, 771–780 (1999). https://doi.org/10.1007/s002080050335
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DOI: https://doi.org/10.1007/s002080050335