Mathematical and physical aspects of complex symmetric operators
  Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, $C$-selfadjoint extensions of $C$-symmetric unbounded operators, resolvent estimates, reality of spectrum, bases of $C$-orthonormal vectors, and conjugate-linear symmetric operators. The main results are complemented by a variety of natural examples arising in field theory, quantum physics, and complex variables. 
Stephan Ramon Garcia, Emil Prodan, Mihai Putinar
math.FA cond-mat.other math-ph math.MP math.OA math.SP