Unbounded complex symmetric operators on Hilbert space are discussed and various spectral results on these operators are presented in this paper. In addition, we show that the technique of complex scaling allows one to identify the quantum resonances of complex self-adjoint Schrödinger Hamiltonians.

Abstract. The purpose of this paper is to introduce, by means of the extensions of almost closed operators, the notion of almost closable linear operator acting in a Hilbert or Banach space. This class of operators is strictly included in the class of all unbounded linear operators, it contains the set of all closable operators and that of all almost closed operators and is invariant under finite and countable sums, finite products, limits and integrals. We also present some fundamental properties relative to almost closability and we define a locally convex Hausdorff topology in the set of all almost closable operators.Mathematics subject classification (2010): 47A05, 47B33.

The paper present a survey of results concerning the fundamental properties of the Drazin inverse for bounded operators and an interesting study of the Drazin inverse for a closed operator in a Banach space. Some necessary and sufficient conditions for $A$ closed linear operator to possess a Drazin inverse $A^D$ are given, we obtain also a useful caracterization and explicit formula for the Drazin inverse $(A+B)^D$ and $(A B)^D$ if $A$ and $B$ are closed operators.