Let P,Q be two linear idempotents on a Banach space. We show that the closedness of the range and complementarity of the kernel (range) of linear combinations of P and Q are independent of the choice of coefficients. This generalizes known results and shows that many spectral properties of linear combinations do not depend on their coefficients.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-3-2,
author = {Hong-Ke Du and Chun-Yan Deng and Mostafa Mbekhta and Vladim\'\i r M\"uller},
title = {On spectral properties of linear combinations of idempotents},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {211-217},
zbl = {1137.47029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-3-2}
}
Hong-Ke Du; Chun-Yan Deng; Mostafa Mbekhta; Vladimír Müller. On spectral properties of linear combinations of idempotents. Studia Mathematica, Tome 178 (2007) pp. 211-217. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-3-2/