Periodic Points of Diagonal and Permutation Operators
Functional Analysis
2025-01-23 v1
Abstract
We first give a condition for a normal operator on a Hilbert space to have no nonzero periodic points, then we give a characterization of normal operators with the whole space as periodic points. We proceed to study the structure of periodic points of the diagonal operators and the permutation operators with examples. Moreover, it is also shown that the set of all diagonal operators with the whole space as periodic points is dense in the set of all unitary diagonal operators.
Cite
@article{arxiv.2501.12605,
title = {Periodic Points of Diagonal and Permutation Operators},
author = {Howen Chuah},
journal= {arXiv preprint arXiv:2501.12605},
year = {2025}
}