Semigroups preserving a convex set in a Banach space
type: Item
instance of: scholarly article
title: Semigroups preserving a convex set in a Banach space
zbMATH Open document ID: 1227.47027
DOI: 10.1215/21562261-1299918
author: Ichiro Shigekawa
published in: Kyoto Journal of Mathematics
publication date: 2011-10-21T00:00:00Z
review text: From the abstract: ``We discuss semigroups that preserve a convex set in a Banach space or a Hilbert space. We give sufficient conditions for which a semigroup preserves a convex set. Using this, we show that various issues can be treated in a unified way. We also discuss the problem in the Hilbert space setting, in which we use the sesquilinear form associated with a semigroup.''
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 47A07
zbMATH DE Number: 5960766
zbMATH Keywords: semigroups preserving a convex set
zbMATH Keywords: Markovian property
zbMATH Keywords: positivity-preserving property
reviewed by: Nguyen Van Minh
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/21562261-1299918
OpenAlex ID: W1964121738
cites work: Semigroups on nonlinear contractions on convex sets
cites work: Feller semigroups, Lp -sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols
cites work: Q3721264
cites work: Pseudo differential operators and Markov processes. In 3 vol. Vol. 1: Fourier analysis and semigroups
cites work: Markov processes associated with semi-Dirichlet forms
cites work: Invariance of closed convex sets and domination criteria for semigroups
description: scientific article; zbMATH DE number 5960766