Regular approximation of singular Sturm–Liouville problems with eigenparameter dependent boundary conditions

In this paper we consider singular Sturm–Liouville problems with eigenparameter dependent boundary conditions and two singular endpoints. The spectrum of such problems can be approximated by those of the inherited restriction operators constructed. Via the abstract operator theory, the strongly resolvent convergence and norm resolvent convergence of a sequence of operators are obtained and it follows that the spectral inclusion of spectrum holds. Moreover, spectral exactness of spectrum holds for two special cases.

Spectral inclusion by the quadratic numerical range of 2 x 2 operator matrices with unbounded entries

This paper deals with the spectral inclusion properties of 2 x 2 operator matrices with unbounded entries in Hilbert space. The conditions for spectral inclusion by the quadratic numerical range are described. In addition, some examples are given to illustrate the main results.

Spectral Inclusions for Quasi-Fredholm and Saphar Spectra for Integrated Semigroups

In this paper, we show a spectral inclusion of integrated semigroups for Saphar, essentially Saphar and quasi-Fredholm spectra.