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/