Taiwanese Journal of Mathematics

EXISTENCE OF A KIND OF BEST SIMULTANEOUS APPROXIMATIONS IN $L_p(\Omega,\Sigma, X)$

X. F. Luo and L. H. Peng

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Abstract

Let $X$ be a Banach space, $Y$ a nonempty locally weakly compact closed convex subset of $X$, $(\Omega,\Sigma,\mu)$ a complete positive $\sigma$-finite measure space and $\Sigma_0$ a sub-$\sigma$-algebra of $\Sigma$. This paper gives existence results of best simultaneous approximations to two functions in $L_p(\Omega,\Sigma,X)$ from $L_p(\Omega,\Sigma,Y)/L_p(\Omega,\Sigma_0,Y)$ if $\overline{{\rm span}\, Y}$/and $\overline{{\rm span}\, Y}^*$ has/have the Radon-Nikodym property.

Article information

Source
Taiwanese J. Math., Volume 16, Number 5 (2012), 1601-1612.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406786

Digital Object Identifier
doi:10.11650/twjm/1500406786

Mathematical Reviews number (MathSciNet)
MR2970674

Zentralblatt MATH identifier
1252.41027

Subjects
Primary: 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

Keywords
simultaneous approximation weak convergence Radon-Nikodym property

Citation

Luo, X. F.; Peng, L. H. EXISTENCE OF A KIND OF BEST SIMULTANEOUS APPROXIMATIONS IN $L_p(\Omega,\Sigma, X)$. Taiwanese J. Math. 16 (2012), no. 5, 1601--1612. doi:10.11650/twjm/1500406786. https://projecteuclid.org/euclid.twjm/1500406786


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