The notion of ball proximinality and the strong ball proximinality were recently introduced in [2]. We prove that a closed * subalgebra A of C(Q) is strongly ball proximinal in C(Q) and the metric projection from C(Q), onto the closed unit ball of A, is Hausdorff metric continuous and hence has continuous selection.
@article{urn:eudml:doc:41866,
title = {Ball proximinality of closed * subalgebras in C(Q)},
journal = {Extracta Mathematicae},
volume = {22},
year = {2007},
pages = {1-17},
zbl = {1161.46004},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41866}
}
Indumathi, V.; Lalithambigai, S.; Lin, Bor-Luh. Ball proximinality of closed * subalgebras in C(Q). Extracta Mathematicae, Tome 22 (2007) pp. 1-17. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41866/