On regulariziers of unbounded linear operators in Banach spaces

Regulariziers of densely defined unbounded linear operators in Banach spaces and their applications to spectral theory are considered. Necessary and sufficient conditions in terms of regularizier properties for an unbounded operator $T$ to be discrete are obtained. In the case when $T$ has a selfadjoint regularizier in some Schatten–von Neumann ideals, asymptotic properties of the eigenvalues are investigated, namely, it is shown that the eigenvalues of $T$ asymptotically belong to a some angle in the complex plane.