APPLICATION OF BISHOP-PHELPS THEOREM IN THE APPROXIMATION THEORY
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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 \(L^1(\Omega,X)\).
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ISRP Style
R. ZARGHAMI, APPLICATION OF BISHOP-PHELPS THEOREM IN THE APPROXIMATION THEORY, Journal of Nonlinear Sciences and Applications, 3 (2010), no. 2, 144 - 147
AMA Style
ZARGHAMI R., APPLICATION OF BISHOP-PHELPS THEOREM IN THE APPROXIMATION THEORY. J. Nonlinear Sci. Appl. (2010); 3(2):144 - 147
Chicago/Turabian Style
ZARGHAMI, R.. "APPLICATION OF BISHOP-PHELPS THEOREM IN THE APPROXIMATION THEORY." Journal of Nonlinear Sciences and Applications, 3, no. 2 (2010): 144 - 147
Keywords
- Bishop-Phelps Theorem
- support point
- proximinality
- L-projection.
MSC
References
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