On some restrictions of an operator to an invariant subspace

For Banach spaces we consider the bounded linear operators which are surjective and noninjective. We show some general properties of such mappings. We examine whether such operators can be restricted to an involution or a projection. Thus, we will show that there exist many invariant subspaces for t...

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Vydáno v:Linear algebra and its applications Ročník 450; s. 1 - 6
Hlavní autor: Wójcik, Paweł
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.06.2014
Témata:
Bounded linear operator
Invariant subspace
Involution
Projection
Involution
Invariant subspace
47A15
47A05
Bounded linear operator
Projection
47A53
ISSN:0024-3795, 1873-1856
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Popis
Shrnutí:For Banach spaces we consider the bounded linear operators which are surjective and noninjective. We show some general properties of such mappings. We examine whether such operators can be restricted to an involution or a projection. Thus, we will show that there exist many invariant subspaces for those operators. In respect to this, we will understand better the structure of many operators.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2014.02.049