| Perturbation Analysis for the Drazin Inverses of Bounded Linear Operators on a Banach Space |
| Received:July 03, 2001 |
| Key Words:
Drazin inverse index error bound.
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| Fund Project:Supported by National Natural Science Foundation of China (19871029) |
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| Abstract: |
| Let X be a Banach space over the complex field C and let T : X→X be a bounded linear operator with Ind(T) = k and R(Tk) closed. Denote the Drazin inverse of T by TD. Let T = T + δT, then TD has the simple expression TD = TD(I + δTTD)-1= (I + TDδT)-1TD under certain hypotheses. The upper bound for the relative error ‖TD-TD‖/‖TD‖and for the solution to the operator equation: Tx = u (u∈R(TD)) is also considered. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2004.03.008 |
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