Instabilité de vecteurs propres d’opérateurs linéaires
1999 ◽
Vol 42
(1)
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pp. 104-117
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Keyword(s):
AbstractWe consider some geometric properties of eigenvectors of linear operators on infinite dimensional Hilbert space. It is proved that the property of a family of vectors (xn) to be eigenvectors of a bounded operator T (admissibility property) is very instable with respect to additive and linear perturbations. For instance, (1) for the sequence to be admissible for every admissible (xn) and for a suitable choice of small numbers it is necessary and sufficient that the perturbation sequence be eventually scalar: there exist such that (Theorem 2); (2) for a bounded operator A to transform admissible families (xn) into admissible families (Axn) it is necessary and sufficient that A be left invertible (Theorem 4).
2006 ◽
Vol 13
(03)
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pp. 239-253
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1986 ◽
Vol 41
(1)
◽
pp. 47-50
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2009 ◽
Vol 80
(1)
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pp. 83-90
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2005 ◽
Vol 79
(3)
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pp. 391-398
1989 ◽
Vol 32
(3)
◽
pp. 320-326
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1996 ◽
Vol 37
(9)
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pp. 4203-4218
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2006 ◽
Vol 09
(02)
◽
pp. 305-314
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