Abstract
The purpose of this note is to examine the following issues related to the Chernoff estimate: (1) For contractions on a Banach space, we modify the [Formula: see text]-estimate and apply it in the proof of the Chernoff product formula for [Formula: see text]-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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