Mathematical and physical aspects of complex symmetric operators (Q2921129)

This is an extensive survey on the theory of complex symmetric operators, accessible to non-specialists. Bounded complex symmetric operators \(T\) on a complex Hilbert space, which satisfy \(T=CT^*C\), where the operator \(C\) is a conjugation. They can also be characterized as those operators which in a suitable orthonormal basis, are represented by a symmetric matrix. The paper contains much information about the spectral theory of these operators, about the extension of the concept to the unbounded case, and about the connection with the theory of \({\mathcal{PT}}\)-symmetric Hamiltonians. Another chapter demonstrates several applications of complex symmetric operators to various problems of mathematical physics. A large list of references is provided.