# APPLICATION OF BISHOP-PHELPS THEOREM IN THE APPROXIMATION THEORY

Volume 3, Issue 2, pp 144 - 147 Publication Date: May 14, 2010
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### Authors

R. ZARGHAMI - Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.

### Abstract

In this paper we apply the Bishop-Phelps Theorem to show that if $X$ is a Banach space and $G\subseteq X$ is a maximal subspace so that $G^\perp = \{x^* \in X^*\mid x^*(y) = 0; \forall y \in G\}$ 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.

•  46E99

### References

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