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 - <p style="text-align: justify;">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 $L^1(\Omega,X)$.</p>