Volume 27, Issue 3
Some Applications of BP-Theorem in Approximation Theory

Anal. Theory Appl., 27 (2011), pp. 220-223.

Published online: 2011-08

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• 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 $L^1(\Omega,X)$.

• Keywords

Bishop-Phelps theorem, support point, proximinality, $L$-projection.

40E09

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@Article{ATA-27-220, author = {}, 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 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 & R. Zarghami. (1970). 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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