Notes on the Chernoff estimate
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-estimate and apply it in the proof of the Chernoff product formula for C0-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.
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