Approximation of semigroups of isometries in a Hilbert space
type: Item
instance of: scholarly article
title: Approximation of semigroups of isometries in a Hilbert space
zbMATH Open document ID: 0998.47023
published in: Russian Mathematics
publication date: 2000-12-07T00:00:00Z
review text: The class of approximating \(C_0\)-semigroups of isometrical operators \((U_t)_{t\geq 0}\) for a given \(C_0\)-semigroup \((V_t)_{t\geq 0}\) in a Hilbert space is introduced as satisfying the condition \[ \|U'_t-V'_t\|_2={\mathcal O}(t^{1/2}), \;t\to 0. \] Here \((U'_t)_{t\geq 0}\) and \((V'_t)_{t\geq 0}\) are minimal unitary dilations. Properties of approximating \(C_0\)-semigroups and their generators are investigated.
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47A20
zbMATH DE Number: 1541584
zbMATH Keywords: isometrical operator
zbMATH Keywords: generator
zbMATH Keywords: cogenerator
zbMATH Keywords: delation
zbMATH Keywords: Hilbert space
zbMATH Keywords: approximating \(C_0\)-semigroups
author: G. G. Amosov
reviewed by: I. V. Melnikova
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1541584