Operator approximations with stable elgenvalues
- 1 October 1990
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- Vol. 49 (2) , 250-257
- https://doi.org/10.1017/s1446788700030524
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
This publication has 1 reference indexed in Scilit:
- A class of strongly stable operator approximationsThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1987