Geodesic
Weak continuity of metric projections
Matematičeskie zametki, Tome 22 (1977) no. 3, pp. 345-356.

Voir la notice de l'article provenant de la source Math-Net.Ru

A necessary and sufficient condition is found for weak continuity of a metric projection onto a finite-dimensional subspace in $l_p$ ($1$). A metric projection onto a boundedly compact set in $l_p$ is sequentially weakly upper semicontinueus. An example is given on a convex, compact set in $l_2$ onto which the metric projection is not weakly continuous. 
@article{MZM_1977_22_3_a3,
     author = {V. S. Balaganskii},
     title = {Weak continuity of metric projections},
     journal = {Matemati\v{c}eskie zametki},
     pages = {345--356},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_3_a3/}
}
TY  - JOUR
AU  - V. S. Balaganskii
TI  - Weak continuity of metric projections
JO  - Matematičeskie zametki
PY  - 1977
SP  - 345
EP  - 356
VL  - 22
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1977_22_3_a3/
LA  - ru
ID  - MZM_1977_22_3_a3
ER  - 
%0 Journal Article
%A V. S. Balaganskii
%T Weak continuity of metric projections
%J Matematičeskie zametki
%D 1977
%P 345-356
%V 22
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1977_22_3_a3/
%G ru
%F MZM_1977_22_3_a3
V. S. Balaganskii. Weak continuity of metric projections. Matematičeskie zametki, Tome 22 (1977) no. 3, pp. 345-356. http://geodesic.mathdoc.fr/item/MZM_1977_22_3_a3/