Spectral Properties of Perturbed Operator
The perturbed operators is given disturbance (perturbation). One of the problems in perturbation theory is to nd the relationship between the eigenvalues and eigenvectors operator which are given perturbation with eigenvalues and eigenvectors are perturbed operator. In [5] have determined the upp...
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| Format: | Theses |
| Language: | Indonesia |
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| Online Access: | https://digilib.itb.ac.id/gdl/view/33762 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | The perturbed operators is given disturbance (perturbation). One of the problems in
perturbation theory is to nd the relationship between the eigenvalues and eigenvectors
operator which are given perturbation with eigenvalues and eigenvectors are perturbed
operator. In [5] have determined the upper bound of the norm perturbation, then [9]
generalization with reduce the upper bound of the norm perturbation. Let T close operator
on Banach space X with domain dense in X and V bounded operators in X, then
T + V perturbed operator and V is perturbation. The upper bound of the norm V will
be sought so that for every r > 0, the operator perturbed T + V has a unique eigenpair
who are in a disc. The perturbed operator T + V has a eigenpair (; ) unique, for every
r > 0 and V 2 L(X) satises kV k
r
c0kS0k(1 + r)2 , where c0 = max fkP0k; kI ???? P0kg. |
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