PreprintarXiv licencearXiv
Non-Elliptic Quadratic π«π―-Symmetric Operators and Similarity to Self-Adjoint Operators
Abstract
We prove a similarity result for non-self-adjoint non-elliptic quadratic π«π―-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.
Related
- Spectral theorem for compact self-adjoint linear relations with an application to elliptic boundary value problems
- Spectral theorem for compact self-adjoint operators on smooth Banach spaces
- Adjoint Closures of Singular Quadratic Pencils and First's Pfister-Type Conjecture
- Intrinsic-dimension empirical Bernstein inequalities for bounded self-adjoint operators
- Weyl's Theorem for Bounded Self-Adjoint Operators
BibTeX
@misc{malkov2026nonelliptic,
title = {{Non-Elliptic Quadratic $\mathcalPT$-Symmetric Operators and Similarity to Self-Adjoint Operators}},
author = {Stepan Malkov},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28821},
eprint = {2608.28821},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28821},
}
RIS
TY - UNPB
TI - Non-Elliptic Quadratic π«π―-Symmetric Operators and Similarity to Self-Adjoint Operators
AU - Stepan Malkov
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28821
UR - https://arxiv.org/abs/2608.28821
AB - We prove a similarity result for non-self-adjoint non-elliptic quadratic π«π―-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.
ER -