On operator-norm approximation of some semigroups by quasi-sectorial operators.
Quasi-sectorial operators were introduced and studied by \textit{V. Cachia} and \textit{V. A. Zagrebnov} [J. Funct. Anal. 180, No. 1, 176--194 (2001; Zbl 0981.47015)]. Among other things, these authors obtained an extension of the famous Chernoff `\(n^{1/2}\)-lemma', with a bound having an order of \(n^{-1/3}\). In the present paper, the authors uses some probabilistic methods to improve bounds for the convergence rates in some approximation formulas for semigroups of contractions. In particular, the bound \(n^{-1/3}\) of Cachia and Zagrebnov is improved to \((\log n/n)^{1/2}\).
scientific article; zbMATH DE number 2062723