Mathematical and physical aspects of complex symmetric operators

Abstract

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.

55 pages; to appear in J. Phys. A: Math. Gen

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Cited by in corpus (10)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Parity-time symmetry in optical microcavity systems
• The essential spectrum of the Neumann--Poincare operator on a domain with corners
• Anti- (Conjugate) Linearity
• Informational power of the Hoggar SIC-POVM
• Complex tridiagonal quantum Hamiltonians and matrix continued fractions
• Level crossing in random matrices. II Random perturbation of a random matrix
• Symmetric and Antisymmetric Tensor Products for the Function-Theoretic Operator Theorist
• On complex symmetric weighted shifts
• A relative Grace Theorem for complex polynomials