Year: 2026
Type: preprint
Abstract: It is shown that a bounded linear map on a complex separable Hilbert space with non-trivial invariant probability measures doesn't have to possess eigenvalues. This resolves a question indicated by Flytzanis in 1995 and concretely asked by Grivaux--López-Martínez from 2023 resp. Grivaux--Matheron--Menet from 2021. Still, as a positive result, we prove that every bounded linear operator on a separable complex Banach space for which a non-fixing invariant probability measure exists, has to have some approximate point spectrum on the unit circle minus $1$.
Source: arXiv (Cornell University)
Author: Steenbeck, Yannic
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212020190