Sub-Markovian semigroups generated by matrix operators
type: Item
instance of: scholarly article
title: Sub-Markovian semigroups generated by matrix operators
zbMATH Open document ID: 0788.47035
DOI: 10.1007/BF01445128
published in: Mathematische Annalen
publication date: 1994-06-05T00:00:00Z
full work available at URL: https://eudml.org/doc/165108
review text: We characterize generators of sub-Markovian semigroups on \(L^ p(\Omega)\) by a version of Kato's inequality. This will be used to show (under precise assumptions) that the semigroup generated by a matrix operator \({\mathcal A}=(A_{ij})_{1\leq i,j\leq n}\) on \((L^ p(\Omega))^ n\) is sub-Markovian if and only if the semigroup generated by the sum of each row \(A_{i1}+\cdots+ A_{in}\) \((1\leq i\leq n)\) is sub-Markovian. The corresponding result on \((C_ 0(X))^ n\) characterizes dissipative operator matrices.
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 47B44
zbMATH DE Number: 537276
zbMATH Keywords: generators of sub-Markovian semigroups
zbMATH Keywords: Kato's inequality
zbMATH Keywords: semigroup generated by a matrix operator
zbMATH Keywords: dissipative operator matrices
author: E. M. Ouhabaz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 537276