The following theorem is the main result of the paper: Let X be a complex Banach space and T belong to L(X). Suppose that 0 lies at the unbounded component of the set of those l such that lI - T is a Fredholm operator. Let Y be a dense subspace of the dual space X' and S be a closed operator from Y to X such that T'(Y) is contained in Y and TSy = ST'y for every y belonging to Y. Then for every vector x belonging to X', T'x belongs to Y if and only if x belongs to Y.
@article{urn:eudml:doc:38777,
title = {Conditions ensuring T-1(Y) [?] Y.},
journal = {Extracta Mathematicae},
volume = {20},
year = {2005},
pages = {43-50},
zbl = {1089.47007},
mrnumber = {MR2149123},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38777}
}
Medková, Dagmar. Conditions ensuring T-1(Y) ⊂ Y.. Extracta Mathematicae, Tome 20 (2005) pp. 43-50. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38777/