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  • Research Article
  • Open Access

A characterization of chaotic order

Journal of Inequalities and Applications20062006:79123

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


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.


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


Authors’ Affiliations

Department of Mathematics, Henan Normal University, Xinxiang, Henan, 453007, China


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© C. Yang and F. Gao 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.