Invariant sublattices
type: Item
instance of: scholarly article
title: Invariant sublattices
zbMATH Open document ID: 1187.47009
author: Vladimir G. Troitsky
author: H. Radjavi
published in: Illinois Journal of Mathematics
publication date: 2009-10-15T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ijm/1248355343
review text: This paper provides a complete characterization of matrices that have invariant sublattices as well as sufficient conditions under which a semigroup of positive matrices has invariant sublattices. Some infinite-dimensional versions of these results in \(\ell^{p}\), \(c_{0},\) or \(L^{p}(\mu),\) are also discussed, including an extension of the Perron-Frobenius theorem. The theory is well illustrated by a number of valuable examples.
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 47B65
zbMATH DE Number: 5615647
zbMATH Keywords: Banach lattice
zbMATH Keywords: positive operator
zbMATH Keywords: invariant sublattice
MaRDI profile type: Publication
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cites work: Q4747037
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cites work: Common invariant subspaces for collections of operators
cites work: Q4108810
cites work: On the invariant subspace problem for Banach spaces
cites work: Q5786104
cites work: Q5494045
cites work: Q4136031
cites work: Q4188284
cites work: Decomposability and structure of nonnegative bands in \({\mathcal M}_n(\mathbb{R})\)
cites work: Q4421991
cites work: Banach lattices
cites work: Q3702832
cites work: The Perron-Frobenius theorem revisited
cites work: Simultaneous triangularization
cites work: A Solution to the Invariant Subspace Problem
cites work: Volterra semigroups have invariant subspaces
cites work: Q4277442
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description: scientific article; zbMATH DE number 5615647