Stability of \(C\)-regularized semigroups
type: Item
instance of: scholarly article
title: Stability of \(C\)-regularized semigroups
zbMATH Open document ID: 1082.47037
author: Miao Li
author: Quan Zheng
publication date: 2005-06-07T00:00:00Z
review text: Let \(X\) be a Banach space, let \(T=\{T(t)\}_{t \geq 0}\) be a bounded \(C\)-regularized semigroup generated by \(A\), where \(C\) is a bounded injective linear operator on \(X\) such that \(R(C)\) is dense in \(X\). Denoting by \(\sigma_u(A, Cx)\) the set of all points \(\lambda \in i {\mathbb R}\) such that \((\lambda - A)^{-1}Cx\) cannot be extended holomorphically, the authors prove that if there exists a dense subspace \(Y \subset X\) such that for every \(x \in Y\), the set \(\sigma_u(A, Cx)\) is at most countable and \(\sigma_r(A) \cap i {\mathbb R} = \emptyset\), then the semigroup \(T\) is stable. The also study the case when \(R(C)\) is non-dense.
reviewed by: Adina Luminiţa Sasu
Mathematics Subject Classification ID: 47D60
Mathematics Subject Classification ID: 47D03
zbMATH DE Number: 2174195
zbMATH Keywords: semigroup
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: s10114-004-0349-8
OpenAlex ID: W2084314495
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DOI: 10.1007/S10114-004-0349-8
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 2174195