Coproximinality in Spaces of Bochner Integrable Functions
Journal of convex analysis, Tome 24 (2017) no. 3, pp. 955-958
In this short note we use a new way of applying von Neumann's selection theorem for obtaining best coapproximation in spaces of measurable functions. For a coproximinal closed subspace $Y$ of a Banach space $X$, we show that if $Y$ is constrained in a weakly compactly generated dual space, then the space $L^1(\mu,Y)$ of $Y$-valued Bochner integrable functions is coproximinal in $L^1(\mu,X)$. This extends a result of M. R. Haddadi, N. Hejazjpoor and H. Mazaheri [{\it Some results about best coapproximation in $L^P(S,X)$}, Anal. Theory Appl. 26 (2010) 69--75], proved when $Y$ is reflexive.
Classification :
41A50, 46B20, 46E40
Mots-clés : Coproximinality, constrained subspaces, weakly compactly generated spaces, spaces of Bochner integrable functions, von Neumann's selection theorem
Mots-clés : Coproximinality, constrained subspaces, weakly compactly generated spaces, spaces of Bochner integrable functions, von Neumann's selection theorem
@article{JCA_2017_24_3_JCA_2017_24_3_a11,
author = {T. S. S. R. K. Rao},
title = {Coproximinality in {Spaces} of {Bochner} {Integrable} {Functions}},
journal = {Journal of convex analysis},
pages = {955--958},
year = {2017},
volume = {24},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_3_JCA_2017_24_3_a11/}
}
T. S. S. R. K. Rao. Coproximinality in Spaces of Bochner Integrable Functions. Journal of convex analysis, Tome 24 (2017) no. 3, pp. 955-958. http://geodesic.mathdoc.fr/item/JCA_2017_24_3_JCA_2017_24_3_a11/