We describe the subspaces of (1 ≤ p ≠ 2 < ∞) which are the range of a completely contractive projection.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-20, author = {Jean Roydor}, title = {Completely 1-complemented subspaces of the Schatten spaces $S^p$ }, journal = {Banach Center Publications}, volume = {75}, year = {2007}, pages = {275-278}, zbl = {1147.47017}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-20} }
Jean Roydor. Completely 1-complemented subspaces of the Schatten spaces $S^p$ . Banach Center Publications, Tome 75 (2007) pp. 275-278. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc78-0-20/