Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

REPRESENTATION OF BOUNDED LINEAR OPERATORS WITH EQUAL SPECTRAL PROJECTIONS AT ZERO

  • Zhang, Yun (DEPARTMENT OF MATHEMATICS HUAIBEI COAL INDUSTRY TEACHERS COLLEGE) ;
  • Chen, Dong-Jun (DEPARTMENT OF MATHEMATICS HUAIBEI COAL INDUSTRY TEACHERS COLLEGE)
  • Received : 2008.08.25
  • Published : 2010.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we present the reprentation of all operators B which are Drazin invertible and sharing the spectral projections at 0 with a given Drazin invertible operator A. Meanwhile, some related results for EP operators with closed range are obtained.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of Anhui

References

  1. A. Ben-Israel and T. Greville, Generalized Inverses: Theory and Applications, Second ed., Springer-Verlag, New York, 2003.
  2. S. L. Campbell, Recent Applications of Generalized Inverses, Pitman, London, 1982.
  3. H.-K. Du and C. Y. Deng, The representation and characterization of Drazin inverses of operators on a Hilbert space, Linear Algebra Appl. 407 (2005), 117–124. https://doi.org/10.1016/j.laa.2005.04.030
  4. N. Castro Gonzalez, J. J. Koliha, and Y. M. Wei, Error bounds for perturbation of the Drazin inverse of closed operators with equal spectral projections, Applicable Analysis 81 (2002), 915–928. https://doi.org/10.1080/0003681021000004474a
  5. N. Castro Gonzalez, J. J. Koliha, and Y. M. Wei, Perturbation of the Drazin inverse for matrices with equal eigenprojections at zero, Linear Algebra Appl. 312 (2000), 181–189. https://doi.org/10.1016/S0024-3795(00)00101-4
  6. N. Castro Gonzalez and J. Velez-Cerrada, Characterizations of matrices whose eigenprojections at zero equal to a fixed perturbation, Appl Math Comput. 159 (2004), 613–623. https://doi.org/10.1016/j.amc.2003.09.027
  7. J. J. Koliha and I. Strasraba, Power bounded and exponentially bounded matrices, Appl. Math. Comput. 44 (1999), 289–308. https://doi.org/10.1023/A:1023032629988
  8. Y. M. Wei, On the perturbation of the group inverse and oblique projections, Appl. Math. Comput. 98 (1999), 29–42. https://doi.org/10.1016/S0096-3003(97)10151-5
  9. Y. M. Wei and G. R. Wang, The perturbation theory for the Drazin inverse and its applications, Linear Algebra Appl. 258 (1997), 179–186. https://doi.org/10.1016/S0024-3795(96)00159-0