Let W and L be complementary subspaces of a Banach space X and let P(W,L) denote the projection on W along L. We obtain a sufficient condition for a subspace M of X to be complementary to W and we derive estimates for the norm of P(W,L) - P(W,M).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-2-6, author = {Gunther Dirr and Vladimir Rako\v cevi\'c and Harald K. Wimmer}, title = {Estimates for projections in Banach spaces and existence of direct complements}, journal = {Studia Mathematica}, volume = {166}, year = {2005}, pages = {211-216}, zbl = {1099.46012}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-2-6} }
Gunther Dirr; Vladimir Rakočević; Harald K. Wimmer. Estimates for projections in Banach spaces and existence of direct complements. Studia Mathematica, Tome 166 (2005) pp. 211-216. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-2-6/