Notes on matrix arithmetic–geometric mean inequalities

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Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory (2005, unknown): “77] or [97].”
Matrix Young inequalities for the Hilbert–Schmidt norm (2000, methodology): “2) in [5] and the Hilbert–Schmidt norm version of the case t = 2 of inequality (5) in [14], and that inequality (16) can be utilized to give direct proofs of the “if ” parts in Corollaries 1–3.”
On an operator Kantorovich inequality for positive linear maps (2012, unknown): “6 ([4]).”
More results on singular value inequalities of matrices (2006, background): “In Theorem 3, inequalities (3) generalize inequalities (5) which are proved by Bhatia and Kittaneh in [8].”
The matrix arithmetic-geometric mean inequality revisited (2008, background): “(5.8) The special case r = 1 was proved by Bhatia and Kittaneh [14], and Tao [36] has proved this for all positive integers r.”
Inequalities for commutators of positive operators (2007, result): “sums, direct sums, and differences of positive operators, we refer to [3,5–7,11,12,14,16–20] and references therein.”
Norm inequalities related to the matrix geometric mean (2012, background): “[15] R. Bhatia, F. Kittaneh, The matrix arithmetic-geometric mean inequality revisited, Linear Algebra Appl.”