Indefinite matrix inequalities via matrix means

Ando, 2004, Löwner inequality of indefinite type, Linear Algebra Appl., 385, 73, 10.1016/S0024-3795(03)00496-8 Ando, 1979 Ando, 1994, Log majorization and complementary Golden-Thompson type inequalities, Linear Algebra Appl., 197/198, 113, 10.1016/0024-3795(94)90484-7 Azizov, 1989, Linear operators in spaces with an indefinite metric Bebiano, 2010, Further developments of Furuta inequality of indefinite type, Math. Inequal. Appl., 13, 523 Bebiano, 2012, Operator inequalities for J-contractions, Math. Inequal. Appl., 12, 883 Bebiano, 2012, On a reverse Heinz-Kato-Furuta inequality, Linear Algebra Appl., 437, 1892, 10.1016/j.laa.2012.05.007 Bognár, 1974, Indefinite Inner Product Spaces, vol. 78 Furuta, 1987, A≥B≥0 assures (BrApBr)1/q≥B(p+2r)/q for r≥0, p≥0, q≥1 with (1+2r)q≥p+2r, Proc. Am. Math. Soc., 101, 85 Dehghani, 2017, Matrix power means and the information monotonicity, Linear Algebra Appl., 521, 57, 10.1016/j.laa.2017.01.025 Ginzburg, 1957, On J-contractive operator functions, Dokl. Akad. Nauk SSSR, 117, 171 Hiai, 2020, Ando-Hiai-type inequalities for operator means and operator perspectives, Int. J. Math., 31, 10.1142/S0129167X2050007X Jakóbczyk, 1985, Canonical quantization with indefinite inner product, Ann. Phys., 161, 314, 10.1016/0003-4916(85)90083-1 Kubo, 1979, Means of positive linear operators, Math. Ann., 246, 205, 10.1007/BF01371042 Moslehian, 2014, Operator convexity in Kreĭn spaces, N.Y. J. Math., 20, 133 Moslehian, 2021, The arithmetic-geometric mean inequality of indefinite type, Arch. Math. (Basel), 10.1007/s00013-021-01615-y Nakazato, 2014, A note on the convexity of the indefinite joint numerical range, Electron. J. Linear Algebra, 27, 705, 10.13001/1081-3810.1962 Potapov, 1982, A Theorem on the Modulus, I: Fundamental Concepts. The Modulus, Teor. Funkc. Funkc. Anal. Ih Prilozh., 38, 91 Sano, 2007, On chaotic order of indefinite type, J. Inequal. Pure Appl. Math., 8 Sano, 2007, Furuta inequality of indefinite type, Math. Inequal. Appl., 10, 381 Wada, 2014, Some ways of constructing Furuta-type inequalities, Linear Algebra Appl., 457, 276, 10.1016/j.laa.2014.05.033 Yamazaki, 2019, The Ando–Hiai inequalities for the solution of the generalized Karcher equation and related results, J. Math. Anal. Appl., 479, 531, 10.1016/j.jmaa.2019.06.036