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ISRN Mathematical Analysis
Volume 2013 (2013), Article ID 145606, 4 pages
http://dx.doi.org/10.1155/2013/145606
Research Article

On the Positive Operator Solutions to an Operator Equation

1School of Mathematics and Computer Science, Shaanxi University of Technology, Shaanxi 723001, China
2College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China

Received 3 May 2013; Accepted 9 June 2013

Academic Editors: M. Lindstrom and K. A. Lurie

Copyright © 2013 Kai-Fan Yang et al. 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. W. Pusz and S. L. Woronowicz, “Functional calculus for sesquilinear forms and the purification map,” Reports on Mathematical Physics, vol. 8, no. 2, pp. 159–170, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J. C. Engwerda, “On the existence of a positive definite solution of the matrix equation X+A*X-αA=I,” Linear Algebra and its Applications, vol. 194, pp. 91–108, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. W. L. Green and E. W. Kamen, “Stabilizability of linear systems over a commutative normed algebra with applications to spatially-distributed and parameter-dependent systems,” SIAM Journal on Control and Optimization, vol. 23, no. 1, pp. 1–18, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. R. S. Bucy, “A priori bounds for the Riccati equation,” in Proceedings of the 6th Berkeley Symposium on Mathematical Statistics and Probability, vol. 111 of Probability Theory, pp. 645–656, University of California Press, Berkeley, Calif, USA, 1972. View at MathSciNet
  5. V. I. Hasanov, Solutions and perturbation theory of nonlinear matrix equations [Ph.D. thesis], Sofia, Bulgaria, 2003.
  6. A. C. M. Ran and M. C. B. Reurings, “On the nonlinear matrix equation X+A*F(X)A=Q: solutions and perturbation theory,” Linear Algebra and its Applications, vol. 346, pp. 15–26, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  7. V. I. Hasanov, “Positive definite solutions of the matrix equations X±A*X-qA=Q,” Linear Algebra and its Applications, vol. 404, pp. 166–182, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. A. C. M. Ran and M. C. B. Reurings, “The symmetric linear matrix equation,” Electronic Journal of Linear Algebra, vol. 9, pp. 93–107, 2002. View at Zentralblatt MATH · View at MathSciNet
  9. K. F. Yang and H. K. Du, “Studies on the positive operator solutions to the operator equations X+A*X-tA=Q,” Acta Mathematica Scientia A, vol. 26, no. 2, pp. 359–364, 2009 (Chinese). View at Zentralblatt MATH · View at MathSciNet
  10. Y. Yang, F. Duan, and X. Zhao, “On solutions for the matrix equation Xs+A*X-tA=Q,” in Proceedings of the 7th International Conference on Matrix Theory and Its Applications in China, pp. 21–24, 2006.
  11. Z.-y. Peng, S. M. El-Sayed, and X.-l. Zhang, “Iterative methods for the extremal positive definite solution of the matrix equation X+A*X-αA=Q,” Journal of Computational and Applied Mathematics, vol. 200, no. 2, pp. 520–527, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Y. Yueting, “The iterative method for solving nonlinear matrix equation Xs+A*X-tA=Q,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 46–53, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. V. I. Hasanov and S. M. El-Sayed, “On the positive definite solutions of nonlinear matrix equation X+A*X-δA=Q,” Linear Algebra and its Applications, vol. 412, no. 2-3, pp. 154–160, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet