On the filling in holes problem for operator matrices

  • Chen X
  • Zhang S
  • Zhong H
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We consider upper-triangular 2-by-2 operator matrices and are interested in the set that has to be added to certain spectra of the matrix in order to get the union of the corresponding spectra of the two diagonal operators. We show that in the cases of the Browder essential approximate point spectrum, the upper semi-Fredholm spectrum, or the lower semi-Fredholm spectrum the set in question need not to be an open set but may be just a singleton. In addition, we modify and extend known results on Hilbert space operators to operators on Banach spaces. © 2008 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • Browder essential approximate point spectrum
  • Lower semi-Fredholm spectrum
  • Operator matrices
  • Upper semi-Fredholm spectrum

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  • Xiaoling Chen

  • Shifang Zhang

  • Huaijie Zhong

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