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 $L^1(\Omega,X)$.