On the orbit of invariant subspaces of linear operators in finite-dimensional spaces (new proof of a Halmos's result)

P.R. Halmos proved that for a linear operator A over a finite-dimensional complex vector space E, every A-invariant subspace of E is the range of a commutant of A. His proof was based on a generalization of the concept of eigenvector. In this note, we give an invariant proof of this Halmos's th...

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Bibliographic Details
Published in:Linear algebra and its applications Vol. 329; no. 1; pp. 171 - 174
Main Author: Faouzi, Abdelkhalek
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 15.05.2001
Elsevier Science
Subjects:
Commutant
Exact sciences and technology
Function theory, analysis
Functor
Invariant subspaces
Mathematical analysis
Mathematical methods in physics
Mathematics
Operator theory
Physics
Sciences and techniques of general use
Invariant subspaces
Functor
47A15
Commutant
Invariant
Invariant subspace
Orbit
Eigenvector
Linear operator
ISSN:0024-3795, 1873-1856
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Summary:P.R. Halmos proved that for a linear operator A over a finite-dimensional complex vector space E, every A-invariant subspace of E is the range of a commutant of A. His proof was based on a generalization of the concept of eigenvector. In this note, we give an invariant proof of this Halmos's theorem.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(01)00239-7