On operator-norm approximation of some semigroups by quasi-sectorial operators.
type: Item
instance of: scholarly article
title: On operator-norm approximation of some semigroups by quasi-sectorial operators.
zbMATH Open document ID: 1068.47047
DOI: 10.1016/S0022-1236(03)00145-9
published in: Journal of Functional Analysis
publication date: 2004-03-29T00:00:00Z
review text: 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 \((\log n/n)^{1/2}\).
Mathematics Subject Classification ID: 47D03
zbMATH DE Number: 2062723
zbMATH Keywords: semigroups of operators
zbMATH Keywords: approximation
zbMATH Keywords: probabilistic methods
author: V. Paulauskas
reviewed by: Cătălin Badea
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2062723