Non-Elliptic Quadratic $\mathcal{PT}$-Symmetric Operators and Similarity to Self-Adjoint Operators
Year: 2026
Type: preprint
Abstract: We prove a similarity result for non-self-adjoint non-elliptic quadratic $\mathcal{PT}$-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.
Source: arXiv (Cornell University)
Author: Malkov, Stepan
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204970976