Year: 2026
Type: preprint
Abstract: Let $10$ such that \[ \|T^N\| \leq C \left( \log(N+1) \right)^κ, \qquad N \geq 1. \] This answers a question raised by Arnold and Cuny concerning positive strongly Kreiss bounded operators on $L^p$-spaces. It also shows that the polynomial exponent appearing in the corresponding problem of Deng, Lorist and Veraar has infimum zero. The proof is elementary: positivity yields a local $\ell^p$-estimate for the orbit on intervals of length of order $\sqrt N$; a positive vector-valued lifting of $T$ then produces a self-improving estimate which can be iterated down to the logarithmic scale.
Source: arXiv (Cornell University)
Author: Arnold, Loris
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214160315