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| METRIC GENERALIZED INVERSE OF LINEAR OPERATOR IN BANACH SPACE |
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Citation： |
WANG Hui,WANG Yuwen.METRIC GENERALIZED INVERSE OF LINEAR OPERATOR IN BANACH SPACE[J].Chinese Annals of Mathematics B,2003,24(4):509~520 |
| Page view： 1873
Net amount： 960 |
Authors： |
WANG Hui; WANG Yuwen |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.19971023) and the
Heilongjiang Provincial Natural Science Foundation of China. |
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| Abstract： |
The Moore-Penrose metric generalized inverse $ T^{+}
$ of linear operator $T$ in Banach space is systematically
investigated in this paper. Unlike the case in Hilbert space, even
$T$ is a linear operator in Banach Space, the Moore-Penrose metric
generalized inverse $ T^{+}$ is usually homogeneous and nonlinear
in general. By means of the methods of geometry of Banach Space,
the necessary and sufficient conditions for existence, continuity,
linearity and minimum property of the Moore-Penrose metric
generalized inverse $T^{+}$ will be given, and some properties of
$T^{+}$ will be investigated in this paper. |
Keywords： |
Banach space, Metric generalized inverse, Generalized orthogonal
decomposition, Homogeneous operator |
Classification： |
46B20 |
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