Some Applications of BP-Theorem in Approximation Theory

Some Applications of BP-Theorem in Approximation Theory

Year:    2011

Analysis in Theory and Applications, Vol. 27 (2011), Iss. 3 : pp. 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 $L^1(\Omega,X)$.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.1007/s10496-011-0220-6

Analysis in Theory and Applications, Vol. 27 (2011), Iss. 3 : pp. 220–223

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    4

Keywords:    Bishop-Phelps theorem support point proximinality $L$-projection.