Skip to content

Advertisement

  • Research Article
  • Open Access

A characterization of chaotic order

Journal of Inequalities and Applications20062006:79123

https://doi.org/10.1155/JIA/2006/79123

  • Received: 15 November 2005
  • Accepted: 4 January 2006
  • Published:

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.

Keywords

  • Hilbert Space
  • Invertible Operator
  • Fixed Positive Number
  • Positive Invertible Operator

[123456]

Authors’ Affiliations

(1)
Department of Mathematics, Henan Normal University, Xinxiang, Henan, 453007, China

References

  1. Ando T: On some operator inequalities. Mathematische Annalen 1987,279(1):157–159. 10.1007/BF01456197MathSciNetView ArticleMATHGoogle Scholar
  2. 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.MathSciNetView ArticleMATHGoogle Scholar
  3. Yamazaki T: Characterizations ofand normaloid operators via Heinz inequality. Integral Equations and Operator Theory 2002,43(2):237–247. 10.1007/BF01200255MathSciNetView ArticleMATHGoogle Scholar
  4. 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.MathSciNetView ArticleMATHGoogle Scholar
  5. Uchiyama M: Some exponential operator inequalities. Mathematical Inequalities & Applications 1999,2(3):469–471.MathSciNetView ArticleMATHGoogle Scholar
  6. Tanahashi K: Best possibility of the Furuta inequality. Proceedings of the American Mathematical Society 1996,124(1):141–146. 10.1090/S0002-9939-96-03055-9MathSciNetView ArticleMATHGoogle Scholar

Copyright

Advertisement