Spectral instability for even non-selfadjoint anharmonic oscillators

We study the instability of the spectrum for a class of non-selfadjoint anharmonic oscillators, estimating the behavior of the instability indices (i. e. the norm of spectral projections) associated with the large eigenvalues of these oscillators. We get asymptotic expansions for the instability indices, extending the results of Davies and Davies-Kuijlaars.