  The purpose of this Note is to highlight the spectral instability of some
non-selfadjoint differential operators, by studying the growth rate of the
norms of the spectral projections $\Pi_n$ associated with their eigenvalues.
More precisely, we are concerned with the complex Airy operator and even
anharmonic oscillator. We get asymptotic expansions for the norm of the
spectral projections associated with the large eigenvalues, extending the
results of Davies and Davies-Kuijlaars.
