DOI QR코드

DOI QR Code

RIGHT AND LEFT FREDHOLM OPERATOR MATRICES

  • Djordjevic, Dragan S. (Faculty of Sciences and Mathematics University of Nis) ;
  • Kolundzija, Milica Z. (Faculty of Sciences and Mathematics University of Nis)
  • Received : 2012.06.13
  • Published : 2013.05.31

Abstract

We consider right and left Fredholm operator matrices of the form $\[\array{A&C\\T&S}\]$, which are linear and bounded on the Banach space $Z=X{\oplus}Y$.

Acknowledgement

Supported by : Ministry of Education and Science

References

  1. D. S. Djordjevic, Perturbations of spectra of operator matrices, J. Operator Theory 48 (2002), no. 3, 467-486.
  2. H. Du and J. Pan, Perturbation of spectrums of $2{\times}2$ operator matrices, Proc. Amer. Math. Soc. 121 (1994), no. 3, 761-766.
  3. B. P. Duggal, Upper triangular operator matrices, SVEP and Browder, Weyl theorems, Integral Equations Operator Theory 63 (2009), no. 1, 17-28. https://doi.org/10.1007/s00020-008-1648-8
  4. G. Hai and A. Chen, Perturbations of the right and left spectra for operator matrices, J. Operator Theory 67 (2012), no. 1, 207-214.
  5. J. K. Han, H. Y. Lee, and W. Y. Lee, Invertible completions of $2{\times}2$ upper triangular operator matrices, Proc. Amer. Math. Soc. 128 (2000), no. 1, 119-123. https://doi.org/10.1090/S0002-9939-99-04965-5
  6. R. Harte, Invertibility and Singularity for Bounded Linear Operators, Marcel Dekker, New York, 1988.
  7. M. Kolundzija, Right invertibility of operator matrices, Funct. Anal. Approx. Comput. 2 (2010), no. 1, 1-5.
  8. W. Y. Lee, Weyl spectra of operator matrices, Proc. Amer. Math. Soc. 129 (2001), no. 1, 131-138. https://doi.org/10.1090/S0002-9939-00-05846-9
  9. V. Muler, Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras, Birkhauser Verlag, Basel-Boston-Berlin, 2007.
  10. C. Tretter, Spectral Theory of Block Operator Matrices and Applications, Imperial College Press, London, 2008.

Cited by

  1. Left- and Right-Atkinson Linear Relation Matrices vol.13, pp.4, 2016, https://doi.org/10.1007/s00009-015-0598-z