Table of Contents
ISRN Applied Mathematics
Volume 2011 (2011), Article ID 846165, 11 pages
http://dx.doi.org/10.5402/2011/846165
Research Article

On the Idempotent Solutions of a Kind of Operator Equations

School of Mathematics Science, South China Normal University, Guangzhou 510631, China

Received 11 March 2011; Accepted 19 April 2011

Academic Editors: F. Messine and F. Tadeo

Copyright © 2011 Chun Yuan Deng. 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. I. Vidav, “On idempotent operators in a Hilbert space,” Publications de l'Institut Mathématique. Nouvelle Série, vol. 4, no. 18, pp. 157–163, 1964. View at Google Scholar · View at Zentralblatt MATH
  2. V. Rakočević, “A note on a theorem of I. Vidav,” Publications de l'Institut Mathématique. Nouvelle Série, vol. 68, no. 82, pp. 105–107, 2000. View at Google Scholar · View at Zentralblatt MATH
  3. C. Schmoeger, “On the operator equations ABA=A2 and BAB=B2,” Publications de l'Institut Mathématique. Nouvelle Série, vol. 78, no. 92, pp. 127–133, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, Wiley-Interscience, New York, NY, USA, 1974. View at Zentralblatt MATH
  5. A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, Springer, New York, NY, USA, 2nd edition, 2002.
  6. C. Y. Deng, “The Drazin inverses of sum and difference of idempotents,” Linear Algebra and Its Applications, vol. 430, no. 4, pp. 1282–1291, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. J. J. Koliha and V. Rakocevic, “Range projections and the Moore-Penrose inverse in rings with involution,” Linear and Multilinear Algebra, vol. 55, no. 2, pp. 103–112, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. G. J. Murphy, C*-Algebra and Operator Theory, Academic Press, New York, NY, USA, 1990.
  9. H. K. Du, “Operator matrix forms of positive operator matrices,” Chinese Quarterly Journal of Mathematics, vol. 7, pp. 9–11, 1992. View at Google Scholar
  10. D. T. Kato, Perturbation Theory for Linear Operators, Springer, New York, NY, USA, 1966.
  11. P. R. Halmos, “Two subspaces,” Transactions of the American Mathematical Society, vol. 144, pp. 381–389, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. C. Y. Deng and H. Du, “A new characterization of the closedness of the sum of two subspaces,” Acta Mathematica Scientia, vol. 28, no. 1, pp. 17–23, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH