Mathematical and physical aspects of complex symmetric operators

Stephan Ramon Garcia, Emil Prodan, Mihai Putinar

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.
Functional Analysis (math.FA); Other Condensed Matter (cond-mat.other); Mathematical Physics (math-ph); Operator Algebras (math.OA); Spectral Theory (math.SP)

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