We prove the stability under compact perturbations of the algebraic index of a Fredholm linear relation with closed range acting between normed spaces. Our main tool is a result concerning the stability of the index of a complex of Banach spaces under compact perturbations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-1-7, author = {Dana Gheorghe}, title = {Stability of the index of a linear relation under compact perturbations}, journal = {Studia Mathematica}, volume = {178}, year = {2007}, pages = {95-102}, zbl = {1119.47013}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-1-7} }
Dana Gheorghe. Stability of the index of a linear relation under compact perturbations. Studia Mathematica, Tome 178 (2007) pp. 95-102. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-1-7/