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/