Abstract
Following an idea of Lin, we prove that if A and B are two positive operators such that 0 < mI ≤ A ≤ m′I ≤ M′I ≤ B ≤ MI, then
and
where \(K\left( h \right) = \frac{{{{\left( {h + 1} \right)}^2}}}{{4h}}\) and \(h = \frac{M}{m}\) and Φ is a positive unital linear map.
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Moradi, H.R., Omidvar, M.E. Complementary inequalities to improved AM-GM inequality. Acta. Math. Sin.-English Ser. 33, 1609–1616 (2017). https://doi.org/10.1007/s10114-017-7118-y
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DOI: https://doi.org/10.1007/s10114-017-7118-y