Volume 15, Issue 2
Approximation theorems of Moore-Penrose inverse by outer inverses

Q. Huang & Z. Fang

Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 15 (2006), pp. 113-119

Published online: 2006-05

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  • Abstract
Let $X$ and $Y$ be Hilbert spaces and $T$ a bounded linear operator from $X$ into $Y$ with a separable range. In this note, we prove, without assuming the closeness of the range of $T$, that the Moore-Penrose inverse $T^+$ of $T$ can be approximated by its bounded outer inverses $T_n^{\#}$ with finite ranks.
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@Article{NM-15-113, author = {Q. Huang and Z. Fang}, title = {Approximation theorems of Moore-Penrose inverse by outer inverses}, journal = {Numerical Mathematics, a Journal of Chinese Universities}, year = {2006}, volume = {15}, number = {2}, pages = {113--119}, abstract = { Let $X$ and $Y$ be Hilbert spaces and $T$ a bounded linear operator from $X$ into $Y$ with a separable range. In this note, we prove, without assuming the closeness of the range of $T$, that the Moore-Penrose inverse $T^+$ of $T$ can be approximated by its bounded outer inverses $T_n^{\#}$ with finite ranks. }, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nm/8020.html} }
TY - JOUR T1 - Approximation theorems of Moore-Penrose inverse by outer inverses AU - Q. Huang & Z. Fang JO - Numerical Mathematics, a Journal of Chinese Universities VL - 2 SP - 113 EP - 119 PY - 2006 DA - 2006/05 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nm/8020.html KW - AB - Let $X$ and $Y$ be Hilbert spaces and $T$ a bounded linear operator from $X$ into $Y$ with a separable range. In this note, we prove, without assuming the closeness of the range of $T$, that the Moore-Penrose inverse $T^+$ of $T$ can be approximated by its bounded outer inverses $T_n^{\#}$ with finite ranks.
Q. Huang & Z. Fang. (1970). Approximation theorems of Moore-Penrose inverse by outer inverses. Numerical Mathematics, a Journal of Chinese Universities. 15 (2). 113-119. doi:
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