## On the limit behavior of the spectrum of a sequence of operators given in various Hilbert spaces.(Russian)Zbl 0684.47002

For separable Hilbert spaces $${\mathcal H}_{\epsilon}$$, $${\mathcal H}_ 0$$ ($$\epsilon$$ is a small parameter), close in a certain sense (defined with the help of operators $$R_{\epsilon}:{\mathcal H}_ 0\to {\mathcal H}_{\epsilon})$$ selfadjoint compact and positive operators $${\mathcal A}_{\epsilon}\in {\mathcal L}({\mathcal H}_{\epsilon})$$ and $${\mathcal A}_ 0\in {\mathcal L}({\mathcal H}_ 0)$$ are considered. If the operators and spaces satisfy the precisely formulated C1-C4 conditions, estimations for convergence of the eigenvalues $$\mu^ k_{\epsilon}-\mu^ k_ 0$$ of operators are given. Similar assertion is proved for the eigenvectors of the operators.
Reviewer: R.Duducava

### MSC:

 47A10 Spectrum, resolvent