Notes on the Chernoff estimate

Notes sur l'estimation de Chernoff Notes sur l'estimation de Chernoff Notes sur l'estimation de Chernoff

Valentin A. Zagrebnov (1)

1 I2M - Institut de Mathématiques de Marseille

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-estimate and apply it in the proof of the Chernoff product formula for C 0-semigroups in the 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 operator-norm estimate for 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 Dunford-Segal approximants.

Mots clés: Semigroup theory; Chernoff lemma; Quasi-sectorial contractions; Product formulae

Domaines: Analyse fonctionnelle [math.FA]

Valentin A. Zagrebnov. Notes on the Chernoff estimate. 2022. ⟨hal-03615863⟩