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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 373147, 8 pages
http://dx.doi.org/10.1155/2013/373147
Research Article

The Intersection of Upper and Lower Semi-Browder Spectrum of Upper-Triangular Operator Matrices

1School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China
2School of Mathematics, Central South University, Changsha 410075, China

Received 22 January 2013; Accepted 3 August 2013

Academic Editor: Alberto Fiorenza

Copyright © 2013 Shifang Zhang 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. X. H. Cao, “Browder spectra for upper triangular operator matrices,” Journal of Mathematical Analysis and Applications, vol. 342, no. 1, pp. 477–484, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. X. H. Cao and B. Meng, “Essential approximate point spectra and Weyl's theorem for operator matrices,” Journal of Mathematical Analysis and Applications, vol. 304, no. 2, pp. 759–771, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. X. L. Chen, S. F. Zhang, and H. J. Zhong, “On the filling in holes problem for operator matrices,” Linear Algebra and its Applications, vol. 430, no. 1, pp. 558–563, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. D. S. Djordjević, “Perturbations of spectra of operator matrices,” Journal of Operator Theory, vol. 48, no. 3, pp. 467–486, 2002. View at Zentralblatt MATH · View at MathSciNet
  5. H. K. Du and P. Jin, “Perturbation of spectrums of 2×2 operator matrices,” Proceedings of the American Mathematical Society, vol. 121, no. 3, pp. 761–766, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S. V. Djordjević and Y. M. Han, “Spectral continuity for operator matrices,” Glasgow Mathematical Journal, vol. 43, no. 3, pp. 487–490, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. G. J. Hai and A. Chen, “Perturbations of the right and left spectra for operator matrices,” Journal of Operator Theory, vol. 67, no. 1, pp. 207–214, 2012. View at Zentralblatt MATH · View at MathSciNet
  8. J. K. Han, H. Y. Lee Youl, and W. Y. Lee Young, “Invertible completions of 2 × 2 upper triangular operator matrices,” Proceedings of the American Mathematical Society, vol. 128, no. 1, pp. 119–123, 2000. View at Publisher · View at Google Scholar · View at Scopus
  9. I. S. Hwang and W. Y. Lee, “The boundedness below of 2×2 upper triangular operator matrices,” Integral Equations and Operator Theory, vol. 39, no. 3, pp. 267–276, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. W. Y. Lee, “Weyl's theorem for operator matrices,” Integral Equations and Operator Theory, vol. 32, no. 3, pp. 319–331, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. W. Y. Lee, “Weyl spectra of operator matrices,” Proceedings of the American Mathematical Society, vol. 129, no. 1, pp. 131–138, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. M. Z. Kolundžija and D. S. Djordjević, “Generalized invertibility of operator matrices,” Arkiv för Matematik, vol. 50, no. 2, pp. 259–267, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Y. Li and H. Du, “The intersection of essential approximate point spectra of operator matrices,” Journal of Mathematical Analysis and Applications, vol. 323, no. 2, pp. 1171–1183, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. E. H. Zerouali and H. Zguitti, “Perturbation of spectra of operator matrices and local spectral theory,” Journal of Mathematical Analysis and Applications, vol. 324, no. 2, pp. 992–1005, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. S. F. Zhang, Z. Y. Wu, and H. J. Zhong, “Continuous spectrum, point spectrum and residual spectrum of operator matrices,” Linear Algebra and its Applications, vol. 433, no. 3, pp. 653–661, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. S. F. Zhang and H. J. Zhong, “A note on Browder spectrum of operator matrices,” Journal of Mathematical Analysis and Applications, vol. 344, no. 2, pp. 927–931, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. S. F. Zhang, H. J. Zhong, and Q. F. Jiang, “Drazin spectrum of operator matrices on the Banach space,” Linear Algebra and its Applications, vol. 429, no. 8-9, pp. 2067–2075, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. S. F. Zhang, H. J. Zhong, and J. D. Wu, “Spectra of 2×2 upper-triangular operator matrices,” Acta Mathematica Sinica, vol. 54, no. 1, pp. 41–60, 2011 (Chinese). View at Zentralblatt MATH · View at MathSciNet
  19. S. F. Zhang, H. J. Zhong, and J. D. Wu, “Fredholm perturbation of spectra of 2×2-upper triangular matrices,” Acta Mathematica Sinica, vol. 54, no. 4, pp. 581–590, 2011 (Chinese). View at MathSciNet
  20. S. F. Zhang and J. D. Wu, “Samuel multiplicities and Browder spectrum of operator matrices,” Operators and Matrices, vol. 6, no. 1, pp. 169–179, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. Y. N. Zhang, H. J. Zhong, and L. Q. Lin, “Browder spectra and essential spectra of operator matrices,” Acta Mathematica Sinica (English Series), vol. 24, no. 6, pp. 947–954, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. S. F. Zhang and Z. Q. Wu, “Characterizations of perturbations of spectra of 2×2 upper triangular operator matrices,” Journal of Mathematical Analysis and Applications, vol. 392, no. 2, pp. 103–110, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. H. Zguitti, “On the Drazin inverse for upper triangular operator matrices,” Bulletin of Mathematical Analysis and Applications, vol. 2, no. 2, pp. 27–33, 2010. View at MathSciNet
  24. X. Fang, “Samuel multiplicity and the structure of semi-Fredholm operators,” Advances in Mathematics, vol. 186, no. 2, pp. 411–437, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. P. A. Fillmore and J. P. Williams, “On operator ranges,” Advances in Mathematics, vol. 7, pp. 254–281, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet