The class of all open linear relations is characterised in terms of the restrictions of the linear relations to finite-codimensional subspaces. As an application, we establish two results, the first of which shows that an upper semi-Fredholm linear relation retains its index under finite rank perturbations, and the second is a density theorem for lower bounded linear relations that have closed range. Results of Labuschagne and of Mbekhta about linear operators are covered.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-3-1,
author = {T. \'Alvarez},
title = {Characterisations of open multivalued linear operators},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {205-212},
zbl = {1108.47003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-3-1}
}
T. Álvarez. Characterisations of open multivalued linear operators. Studia Mathematica, Tome 173 (2006) pp. 205-212. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-3-1/