Conditions ensuring T-1(Y) ⊂ Y.

@article{Medková2005,
abstract = {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.},
author = {Medková, Dagmar},
journal = {Extracta Mathematicae},
keywords = {complex Banach space; Fredholm operator; closed operator; Plemejl's triplet},
language = {eng},
number = {1},
pages = {43-50},
title = {Conditions ensuring T-1(Y) ⊂ Y.},
url = {http://eudml.org/doc/38777},
volume = {20},
year = {2005},
}

TY - JOUR
AU - Medková, Dagmar
TI - Conditions ensuring T-1(Y) ⊂ Y.
JO - Extracta Mathematicae
PY - 2005
VL - 20
IS - 1
SP - 43
EP - 50
AB - 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.
LA - eng
KW - complex Banach space; Fredholm operator; closed operator; Plemejl's triplet
UR - http://eudml.org/doc/38777
ER -