Notes on the Chernoff estimate
Functional Analysis
2022-10-26 v1
Abstract
The purpose of the present notes is to examine the following issues related to the the Chernoff estimate: (1) For contractions on a Banach space we modify the -estimate and apply it in the proof of the Chernoff product formula for -semigroups in the \textit{strong} operator topology. (2) We use the idea of a {probabilistic} approach, proving the Chernoff estimate in the strong operator topology, to uplift it to the \textit{operator-norm} estimate for \textit{quasi-sectorial} contraction semigroups. (3) The operator-norm Chernoff estimate is applied to {quasi-sectorial} contraction semigroups for proving the operator-norm convergence of the \textit{Dunford-Segal} approximants.
Cite
@article{arxiv.2205.04794,
title = {Notes on the Chernoff estimate},
author = {Valentin A. Zagrebnov},
journal= {arXiv preprint arXiv:2205.04794},
year = {2022}
}