# Conditions ensuring T-1(Y) ⊂ Y.

Extracta Mathematicae (2005)

- Volume: 20, Issue: 1, page 43-50
- ISSN: 0213-8743

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topMedková, Dagmar. "Conditions ensuring T-1(Y) ⊂ Y.." Extracta Mathematicae 20.1 (2005): 43-50. <http://eudml.org/doc/38777>.

@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 -

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