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Volume 31, Issue 4
The Representive of Metric Projection on the Finite Codimension Subspace in Banach Space

Xiaobin Liang & Shixiang Huang

Commun. Math. Res., 31 (2015), pp. 373-382.

Published online: 2021-05

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  • Abstract

In the paper we introduce the notions of the separation factor $κ$ and give a representive of metric projection on an $n$-codimension subspace (or an affine set) under certain conditions in Banach space. Further, we obtain the distance formula from any point $x$ to a finite $n$-codimension subspace. Results extend and improve the corresponding results in Hilbert space.

  • Keywords

$n$-codimension, separation factor $κ$, weakly completely separated.

  • AMS Subject Headings

41A65, 46B20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-31-373, author = {Xiaobin and Liang and and 19029 and and Xiaobin Liang and Shixiang and Huang and and 18765 and and Shixiang Huang}, title = {The Representive of Metric Projection on the Finite Codimension Subspace in Banach Space}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {4}, pages = {373--382}, abstract = {

In the paper we introduce the notions of the separation factor $κ$ and give a representive of metric projection on an $n$-codimension subspace (or an affine set) under certain conditions in Banach space. Further, we obtain the distance formula from any point $x$ to a finite $n$-codimension subspace. Results extend and improve the corresponding results in Hilbert space.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.04.09}, url = {http://global-sci.org/intro/article_detail/cmr/18920.html} }
TY - JOUR T1 - The Representive of Metric Projection on the Finite Codimension Subspace in Banach Space AU - Liang , Xiaobin AU - Huang , Shixiang JO - Communications in Mathematical Research VL - 4 SP - 373 EP - 382 PY - 2021 DA - 2021/05 SN - 31 DO - http://doi.org/10.13447/j.1674-5647.2015.04.09 UR - https://global-sci.org/intro/article_detail/cmr/18920.html KW - $n$-codimension, separation factor $κ$, weakly completely separated. AB -

In the paper we introduce the notions of the separation factor $κ$ and give a representive of metric projection on an $n$-codimension subspace (or an affine set) under certain conditions in Banach space. Further, we obtain the distance formula from any point $x$ to a finite $n$-codimension subspace. Results extend and improve the corresponding results in Hilbert space.

Xiaobin Liang & Shixiang Huang. (2021). The Representive of Metric Projection on the Finite Codimension Subspace in Banach Space. Communications in Mathematical Research . 31 (4). 373-382. doi:10.13447/j.1674-5647.2015.04.09
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