ON BEST APPROXIMATIONS IN THE LEBESGUE-BOCHNER SPACE $L^1(X)$

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Published: Sep 1, 1993
DOI: https://doi.org/10.5556/j.tkjm.24.1993.4501
Keywords:
Proximal set best approximation Lebesgue-Bochner space

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NIKOLAOS S. PAPAGEORGIOU
National Technical University, Department of Machcmatics, Zografou Campus, Athens 15773, Greece.

Abstract




If $\Sigma_0\subseteq \Sigma$ is a sub-$\sigma$-field and $X$ a reflexive Banach space, we show that the Lebesgue-Bochner space $L^1(\Sigma_0, X )$ is proximinal in $L^1(\Sigma, X)$. Then we examine how the set of best approximations and the distance function depend on $\Sigma_0$.




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How to Cite
PAPAGEORGIOU, N. S. (1993). ON BEST APPROXIMATIONS IN THE LEBESGUE-BOCHNER SPACE $L^1(X)$. Tamkang Journal of Mathematics, 24(3), 303–307. https://doi.org/10.5556/j.tkjm.24.1993.4501
Issue
Vol. 24 No. 3 (1993)
Section
Papers
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Author Biography

NIKOLAOS S. PAPAGEORGIOU, National Technical University, Department of Machcmatics, Zografou Campus, Athens 15773, Greece.

Mailing address: Florida Institute of Technology, Department of Applied Mathematics, 150 West University Blvd., Melbourne, Florida 32901-6988, U. S. A.

References

J. Diestel and J. Uhl, "Vector Measures", Math Surveys, Vol. 15, AMS, Providence, RI (1977).

M. Metivier, "Semimatringales", DeGruyter, Berlin (1982).

T. Shintani and T. Ando, "Best approximations in L^1-space", Z. Wahnihein Verw, Gabiete 33 (1975), 33-39.