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A characterization of chaotic order
Journal of Inequalities and Applications volume 2006, Article number: 79123 (2006)
Abstract
The chaotic order among positive invertible operators
on a Hilbert space is introduced by
. Using Uchiyama's method and Furuta's Kantorovich-type inequality, we will point out that
if and only if
holds for any
, where
is any fixed positive number. On the other hand, for any fixed
, we also show that there exist positive invertible operators
,
such that
holds for any
, but
is not valid.
References
Ando T: On some operator inequalities. Mathematische Annalen 1987,279(1):157–159. 10.1007/BF01456197
Fujii M, Furuta T, Kamei E: Furuta's inequality and its application to Ando's theorem. Linear Algebra and Its Applications 1993, 179: 161–169.
Yamazaki T: Characterizations ofand normaloid operators via Heinz inequality. Integral Equations and Operator Theory 2002,43(2):237–247. 10.1007/BF01200255
Furuta T: Results undercan be derived from ones underby Uchiyama's method—associated with Furuta and Kantorovich type operator inequalities. Mathematical Inequalities & Applications 2000,3(3):423–436.
Uchiyama M: Some exponential operator inequalities. Mathematical Inequalities & Applications 1999,2(3):469–471.
Tanahashi K: Best possibility of the Furuta inequality. Proceedings of the American Mathematical Society 1996,124(1):141–146. 10.1090/S0002-9939-96-03055-9
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Yang, C., Gao, F. A characterization of chaotic order. J Inequal Appl 2006, 79123 (2006). https://doi.org/10.1155/JIA/2006/79123
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DOI: https://doi.org/10.1155/JIA/2006/79123