Some Applications of BP-Theorem in Approximation Theory
Anal. Theory Appl., 27 (2011), pp. 220-223.
Published online: 2011-08
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@Article{ATA-27-220,
author = {I. Sadeqi and R. Zarghami},
title = {Some Applications of BP-Theorem in Approximation Theory},
journal = {Analysis in Theory and Applications},
year = {2011},
volume = {27},
number = {3},
pages = {220--223},
abstract = {
In this paper we apply Bishop-Phelps property to show that if $X$ is a Banach space and $G \subseteq X$ is the maximal subspace so that $G^\bot = \{x^* \in X^*|x^*(y) = 0; \forall y \in G\}$ is an $L$-summand in $X^*$, then $L^1(\Omega,G)$ is contained in a maximal proximinal subspace of $L^1(\Omega,X)$.
}, issn = {1573-8175}, doi = {https://doi.org/10.1007/s10496-011-0220-6}, url = {http://global-sci.org/intro/article_detail/ata/4595.html} }
TY - JOUR
T1 - Some Applications of BP-Theorem in Approximation Theory
AU - I. Sadeqi & R. Zarghami
JO - Analysis in Theory and Applications
VL - 3
SP - 220
EP - 223
PY - 2011
DA - 2011/08
SN - 27
DO - http://doi.org/10.1007/s10496-011-0220-6
UR - https://global-sci.org/intro/article_detail/ata/4595.html
KW - Bishop-Phelps theorem, support point, proximinality, $L$-projection.
AB -
In this paper we apply Bishop-Phelps property to show that if $X$ is a Banach space and $G \subseteq X$ is the maximal subspace so that $G^\bot = \{x^* \in X^*|x^*(y) = 0; \forall y \in G\}$ is an $L$-summand in $X^*$, then $L^1(\Omega,G)$ is contained in a maximal proximinal subspace of $L^1(\Omega,X)$.
I. Sadeqi and R. Zarghami. (2011). Some Applications of BP-Theorem in Approximation Theory.
Analysis in Theory and Applications. 27 (3).
220-223.
doi:10.1007/s10496-011-0220-6
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