Hermitian and positive \(C\)-semigroups on Banach spaces
type: Item
instance of: scholarly article
title: Hermitian and positive \(C\)-semigroups on Banach spaces
zbMATH Open document ID: 0845.47029
author: Yuan-Chuan Li
author: Sen-Yen Shaw
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1996-09-01T00:00:00Z
review text: Summary: Two classes of operator families, namely \(n\)-times integrated \(C\)-semigroups of hermitian and positive operators on Banach spaces, are studied. By using Gelfand transform and a theorem of Sinclair, we prove some interesting special properties of such \(C\)-semigroups. For instances, every hermitian nondegenerate \(n\)-times integrated \(C\)-semigroup on a reflexive space is the \(n\)-times integral of some hermitian \(C\)-semigroup with a densely defined generator; an exponentially bounded \(C\)-semigroup on \(L^p (\mu)\) \((1<p< \infty)\) dominates \(C\) (a positive injective operator) if and only if its generator \(A\) is bounded, positive, and commutes with \(C\); when \(C\) has dense range, the latter assertion is also true on \(L^1 (\mu)\) and \(C_0 (\Omega)\).
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47B15
Mathematics Subject Classification ID: 47A12
zbMATH DE Number: 878493
zbMATH Keywords: \(n\)-times integrated \(C\)-semigroups of hermitian and positive operators on Banach spaces
zbMATH Keywords: Gelfand transform
zbMATH Keywords: exponentially bounded \(C\)-semigroup
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195163918
OpenAlex ID: W2129319734
DOI: 10.2977/PRIMS/1195163918
description: scientific article; zbMATH DE number 878493