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Abstract and Applied Analysis
Volume 2014, Article ID 457367, 7 pages
http://dx.doi.org/10.1155/2014/457367
Research Article

Some Properties of Furuta Type Inequalities and Applications

School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan 454000, China

Received 25 January 2014; Accepted 20 March 2014; Published 13 April 2014

Academic Editor: Changsen Yang

Copyright © 2014 Jiangtao Yuan and Caihong Wang. 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.

Linked References

  1. R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras, American Mathematical Society, Providence, RI, USA, 1997.
  2. T. Furuta, Invitation to Linear Operators, Taylor & Francis, London, UK, 2001. View at MathSciNet
  3. T. Furuta, “AB0 assures (BrApBr)1/qBp+2r/q for r0,p0,q1 with (1+2r)qp+2r,” Proceedings of the American Mathematical Society, vol. 101, no. 1, pp. 85–88, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  4. J. Yuan and Z. Gao, “Complete form of Furuta inequality,” Proceedings of the American Mathematical Society, vol. 136, no. 8, pp. 2859–2867, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  5. J.-C. Bourin and E. Ricard, “An asymmetric Kadison's inequality,” Linear Algebra and Its Applications, vol. 433, no. 3, pp. 499–510, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  6. S. R. Garcia, “Aluthge transforms of complex symmetric operators,” Integral Equations and Operator Theory, vol. 60, no. 3, pp. 357–367, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  7. V. Lauric, “(Cp,α)-hyponormal operators and trace-class self-commutators with trace zero,” Proceedings of the American Mathematical Society, vol. 137, no. 3, pp. 945–953, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  8. M. Ito, T. Yamazaki, and M. Yanagida, “Generalizations of results on relations between Furuta-type inequalities,” Acta Scientiarum Mathematicarum, vol. 69, no. 3-4, pp. 853–862, 2003. View at Google Scholar · View at MathSciNet
  9. M. Ito and T. Yamazaki, “Relations between two inequalities (Br/2ApBr/2)r/p+rBr and (Ap/2BrAp/2)p/p+rAp and their applications,” Integral Equations and Operator Theory, vol. 44, no. 4, pp. 442–450, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  10. T. Furuta, “Extension of the Furuta inequality and Ando-Hiai log-majorization,” Linear Algebra and Its Applications, vol. 219, pp. 139–155, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  11. M. Fujii, R. Nakamoto, and K. Yonezawa, “A satellite of the grand Furuta inequality and Its application,” Linear Algebra and Its Applications, vol. 438, no. 4, pp. 1580–1586, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  12. M. Fujii, E. Kamei, and R. Nakamoto, “Grand Furuta inequality and its variant,” Journal of Mathematical Inequalities, vol. 1, no. 3, pp. 437–441, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  13. P. Lancaster and L. Rodman, The Algebraic Riccati Equation, Academic Press, Oxford, UK, 1995.
  14. G. K. Pedersen and M. Takesaki, “The operator equation THT=K,” Proceedings of the American Mathematical Society, vol. 36, pp. 311–312, 1972. View at Google Scholar · View at MathSciNet
  15. J. Yuan and Z. Gao, “The operator equation Kp=Hδ/2T1/2(T1/2Hδ+rT1/2)p-δ/δ+rT1/2Hδ/2 and its applications,” Journal of Mathematical Analysis and Applications, vol. 341, no. 2, pp. 870–875, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  16. J. T. Yuan and C. H. Wang, “Riccati type operator equation and Furuta's question,” Mathematical Inequalities & Application. In press.
  17. J. Yuan, “Furuta inequality and q-hyponormal operators,” Operators and Matrices, vol. 4, no. 3, pp. 405–415, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  18. J. Yuan and G. Ji, “Monotonicity of generalized Furuta type functions,” Operators and Matrices, vol. 6, no. 4, pp. 809–818, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  19. C. S. Yang and J. T. Yuan, “Class wF(p,r,q) operators,” Acta Mathematica Scientia A, vol. 27, no. 5, pp. 769–780, 2007. View at Google Scholar · View at MathSciNet
  20. R. Bhatia and M. Uchiyama, “The operator equation i=0nAn-iXBi=Y,” Expositiones Mathematicae, vol. 27, no. 3, pp. 251–255, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  21. M. Yanagida, “Powers of class wA(s,t) operators associated with generalized Aluthge transformation,” Journal of Inequalities and Applications, vol. 7, no. 2, pp. 143–168, 2002. View at Publisher · View at Google Scholar · View at MathSciNet