English

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 n\sqrt{n}-estimate and apply it in the proof of the Chernoff product formula for C0C_0-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.

Keywords

Cite

@article{arxiv.2205.04794,
  title  = {Notes on the Chernoff estimate},
  author = {Valentin A. Zagrebnov},
  journal= {arXiv preprint arXiv:2205.04794},
  year   = {2022}
}
R2 v1 2026-06-24T11:12:54.601Z