About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 461567, 7 pages
http://dx.doi.org/10.1155/2014/461567
Research Article

On Subscalarity of Some 2 × 2 M-Hyponormal Operator Matrices

1College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, Henan, China
2School of Mathematical Science, Inner Mongolia University, Hohhot 010021, Inner Mongolia, China

Received 25 December 2013; Accepted 16 January 2014; Published 25 February 2014

Academic Editor: Yisheng Song

Copyright © 2014 Fei Zuo and Junli Shen. 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. Harte, Invertibility and Singularity for Bounded Linear Operators, Marcel Dekker, New York, NY, USA, 1988. View at MathSciNet
  2. R. Harte and W. Y. Lee, “Another note on Weyl's theorem,” Transactions of the American Mathematical Society, vol. 349, no. 5, pp. 2115–2124, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. X. Cao, M. Guo, and B. Meng, “Weyl type theorems for p-hyponormal and M-hyponormal operators,” Studia Mathematica, vol. 163, no. 2, pp. 177–188, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  4. R. L. Moore, D. D. Rogers, and T. T. Trent, “A note on intertwining M-hyponormal operators,” Proceedings of the American Mathematical Society, vol. 83, no. 3, pp. 514–516, 1981. View at Publisher · View at Google Scholar · View at MathSciNet
  5. A. Uchiyama and T. Yoshino, “Weyl's theorem for p-hyponormal or M-hyponormal operators,” Glasgow Mathematical Journal, vol. 43, no. 3, pp. 375–381, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  6. M. Putinar, “Hyponormal operators are subscalar,” Journal of Operator Theory, vol. 12, no. 2, pp. 385–395, 1984. View at Zentralblatt MATH · View at MathSciNet
  7. S. W. Brown, “Hyponormal operators with thick spectra have invariant subspaces,” Annals of Mathematics, vol. 125, no. 1, pp. 93–103, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. S. Jung, Y. Kim, and E. Ko, “On subscalarity of some 2×2 class A operator matrices,” Linear Algebra and Its Applications, vol. 438, no. 3, pp. 1322–1338, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Jung, E. Ko, and M.-J. Lee, “On class A operators,” Studia Mathematica, vol. 198, no. 3, pp. 249–260, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. Jung, E. Ko, and M.-J. Lee, “Subscalarity of (p,k)-quasihyponormal operators,” Journal of Mathematical Analysis and Applications, vol. 380, no. 1, pp. 76–86, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  11. E. Ko, “kth roots of p-hyponormal operators are subscalar operators of order 4k,” Integral Equations and Operator Theory, vol. 59, no. 2, pp. 173–187, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  12. K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, Clarendon Press, Oxford, UK, 2000. View at MathSciNet
  13. M. Oudghiri, “Weyl's and Browder's theorems for operators satisfying the SVEP,” Studia Mathematica, vol. 163, no. 1, pp. 85–101, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. P. Aiena, M. Chō, and M. González, “Polaroid type operators under quasi-affinities,” Journal of Mathematical Analysis and Applications, vol. 371, no. 2, pp. 485–495, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. P. Aiena, E. Aponte, and E. Balzan, “Weyl type theorems for left and right polaroid operators,” Integral Equations and Operator Theory, vol. 66, no. 1, pp. 1–20, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet