Article contents
Operator approximations with stable elgenvalues
Published online by Cambridge University Press: 09 April 2009
Abstract
Suppose λ is an isolated eigenvalue of the (bounded linear) operator T on the Banach space X and the algebraic multiplicity of λ is finite. Let Tn be a sequence of operators on X that converge to T pointwise, that is, Tnx → Tx for every x ∈ X. If ‖(T − Tn)Tn‖ and ‖Tn(T − Tn)‖ converge to 0 then Tn is strongly stable at λ.
Keywords
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 1990
References
- 4
- Cited by