Non-Elliptic Quadratic PT-Symmetric Operators and Similarity to Self-Adjoint Operators
Stepan Malkov
Abstract
We prove a similarity result for non-self-adjoint non-elliptic quadratic PT-symmetric operators with real spectrum satisfying a dynamical averaging condition. In particular, we show that such an operator is weakly similar to a self-adjoint operator precisely when the fundamental matrix of the associated quadratic form is diagonalizable.
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