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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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