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.

http://arxiv.org/abs/1404.1304
Functional Analysis (math.FA); Other Condensed Matter (cond-mat.other); Mathematical Physics (math-ph); Operator Algebras (math.OA); Spectral Theory (math.SP)