Comments on the Trotter product formula error-bound estimates for non-selfadjoint semigroups
type: Item
instance of: scholarly article
title: Comments on the Trotter product formula error-bound estimates for non-selfadjoint semigroups
zbMATH Open document ID: 1036.47024
DOI: 10.1007/BF01270921
author: Vincent Cachia
author: Hagen Neidhardt
author: V. A. Zagrebnov
published in: Integral Equations and Operator Theory
publication date: 2003-11-03T00:00:00Z
review text: Let \(A\) be a positive selfadjoint operator in a separable Hilbert space. Let \(B\) be an \(m\)-accretive operator which is relatively bounded with respect to \(A\) with bound less than one. Then \(H=A+B\) is \(m\)-accretive. If \(B\) is strictly \(m\)-accretive and \(D((H^\ast)^\alpha)\subset D(A^\alpha)\cap D((B^\ast)^\alpha)\not=\{0\}\) for some \(\alpha\in (0,1]\), then \(\| (e^{-tB/n}e^{-tA/n})^n-e^{-tH}\| =O(\ln n/n^\alpha)\) as \(n\rightarrow \infty\), uniformly in \(t\geq 0\).
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 35K22
Mathematics Subject Classification ID: 41A80
zbMATH DE Number: 1754749
zbMATH Keywords: Trotter product formula
zbMATH Keywords: error bound
zbMATH Keywords: separable Hilbert space
zbMATH Keywords: \(m\)-accretive operator
reviewed by: V. A. Liskevich
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1754749