Sums of order bounded disjointness preserving linear operators
type: Item
instance of: scholarly article
title: Sums of order bounded disjointness preserving linear operators
zbMATH Open document ID: 1437.47018
DOI: 10.1134/S0037446619010130
published in: Siberian Mathematical Journal
publication date: 2019-07-12T00:00:00Z
review text: The authors study the possibility of decomposing an order bounded $n$-disjoint operator into a sum of disjointness preserving operators. It turns out that such a decomposition is unique up to some ``Boolea- valued permutation''. Namely, the authors define a purely $n$-disjoint linear operator $T : E \to F$ between real vector lattices $E$ and $F$ if $n$ is the least natural for which $T$ is $n$-disjoint for all nonzero band projections in the second annihilator of $T(E)$. This concept proves fruitful for formulating the Boolean-valued analogue of permutations that yield the desired decompositions.
Mathematics Subject Classification ID: 47B65
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 47A65
zbMATH DE Number: 7079966
zbMATH Keywords: vector lattice
zbMATH Keywords: purely \(n\)-disjoint operator
zbMATH Keywords: Boolean permutation
zbMATH Keywords: factorization
zbMATH Keywords: disjointness preserving operator
author: Anatoly G. Kusraev
author: Zalina Kusraeva
reviewed by: S. S. Kutateladze
MaRDI profile type: Publication
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full work available at URL: s0037446619010130
OpenAlex ID: W2938319285
Wikidata QID: Q128052333
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description: scientific article; zbMATH DE number 7079966