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A refinement of the grand Furuta inequality. (English) Zbl 1507.47038

Summary: A refinement of the Löwner-Heinz inequality has been discussed by M. S. Moslehian and H. Najafi [Linear Algebra Appl. 437, No. 9, 2359–2365 (2012; Zbl 1272.47027)]. In a preceding paper [Banach J. Math. Anal. 8, No. 2, 118–123 (2014; Zbl 1304.47024)], we improved it and extended to the Furuta inequality. In this note, we give a further extension for the grand Furuta inequality. We also discuss it for operator means. A refinement of the arithmetic-geometric mean inequality is obtained.

MSC:

47A63 Linear operator inequalities
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
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Full Text: Euclid