Balanced exponential growth of operator semigroups
type: Item
instance of: scholarly article
title: Balanced exponential growth of operator semigroups
zbMATH Open document ID: 0943.47032
author: Horst R. Thieme
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-09-11T00:00:00Z
review text: A \(C_0\)-semigroup \(S(t)\), \(t\geq 0\), on a Banach space \(X\) (weakly, strongly, uniformly) approaches balanced (or asynchronous) exponential growth if there exists some \(s\in\mathbb{R}\) such that \[ P= \lim_{t\to\infty} e^{-st}S(t) \] exists (in the weak, strong, uniform operator topology) and \(P\) is not the \(0\) operator. The author characterizes the strong and uniform approach to balanced exponential growth and derives applicable sufficient conditions.
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 1215659
zbMATH Keywords: dual semigroups
zbMATH Keywords: essentially norm-continuous semigroups
zbMATH Keywords: Cauchy problems
zbMATH Keywords: positive perturbations
zbMATH Keywords: \(C_0\)-semigroup
zbMATH Keywords: exponential growth
MaRDI profile type: Publication
full work available at URL: jmaa.1998.5952
OpenAlex ID: W2000768866
cites work: Tauberian Theorems and Stability of One-Parameter Semigroups
cites work: Vector-Valued Tauberian Theorems and Asymptotic Behavior of Linear Volterra Equations
cites work: Stability of Individual Elements Under One-Parameter Semigroups
cites work: Q3776123
cites work: A characterization of sun-reflexivity
cites work: Q5512461
cites work: One-parameter semigroups of positive operators
cites work: The size and scar distributions of the yeast Saccharomyces cerevisiae
cites work: Semigroup Theory for Control on Sun-reflexive Banach Spaces
cites work: Q3743912
cites work: Q3244654
cites work: Q4127752
cites work: The deterministic evolution of general branching populations
cites work: Asymptotic behavior of successive iterates of continuous functions under a Markov operator
cites work: Q4110164
cites work: Subadditive mean ergodic theorems
cites work: Asymptotic stability of linear differential equations in Banach spaces
cites work: \(C_0\)-semigroups norm continuous at infinity
cites work: Q4723599
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Q5516366
cites work: Q4042131
cites work: Q4715322
cites work: Positive perturbation of operator semigroups: Growth bounds, essential compactness, and asynchronous exponential growth
cites work: Balanced exponential growth for perturbed operator semigroups
cites work: A Converse of Lotz's Theorem on Uniformly Continuous Semigroups
cites work: Individual stability of \(C_0\)-semigroups with uniformly bounded local resolvent
cites work: Q3220397
cites work: An Operator-Theoretic Formulation of Asynchronous Exponential Growth
DOI: 10.1006/JMAA.1998.5952
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description: scientific article; zbMATH DE number 1215659