Monomial decomposition of homogeneous polynomials in vector lattices
type: Item
instance of: scholarly article
title: Monomial decomposition of homogeneous polynomials in vector lattices
zbMATH Open document ID: 1440.46042
author: Anatoly G. Kusraev
author: Zalina Kusraeva
published in: Advances in Operator Theory
publication date: 2019-01-31T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.aot/1543633236
review text: This paper is inspired by the two papers [\textit{D. C. Carothers} and \textit{W. A. Feldman}, J. Oper. Theory 24, No. 2, 337--349 (1990; Zbl 0784.47041)] and [\textit{S. J. Bernau} et al., Proc. Am. Math. Soc. 115, No. 1, 151--156 (1992; Zbl 0780.46004)]. The authors generalize the available results to the multilinear case and find some necessary and sufficient conditions for a homogeneous polynomial between vector lattices to be a linear combination of monomials in lattice homomorphisms.
Mathematics Subject Classification ID: 46G25
Mathematics Subject Classification ID: 47H60
Mathematics Subject Classification ID: 46A40
zbMATH DE Number: 7009318
zbMATH Keywords: vector lattice
zbMATH Keywords: multilinear operator
zbMATH Keywords: homogeneous polynomial
zbMATH Keywords: factorization
reviewed by: S. S. Kutateladze
MaRDI profile type: Publication
OpenAlex ID: W2893601825
cites work: Q3748810
cites work: Orthogonally Additive Homogenous Polynomials on Vector Lattices
cites work: Sums of Lattice Homomorphisms
cites work: Q4814345
cites work: Some aspects of Riesz multimorphisms
cites work: Vector Lattice Powers:f-Algebras and Functional Calculus
cites work: Polynomials on Banach lattices and positive tensor products
cites work: Q5263140
cites work: Almost \(f\)-algebras: Commutativity and the Cauchy-Schwarz inequality
cites work: Squares of Riesz spaces
cites work: Bounded variation and tensor products of Banach lattices
cites work: Q4010064
cites work: Q4257163
cites work: Q4891410
cites work: Q4888394
cites work: A representation theorem for orthogonally additive polynomials on Riesz spaces
cites work: Q4841573
cites work: Boolean valued analysis. Selected topics
cites work: Q5476802
cites work: Q3545572
cites work: Sums of order bounded disjointness preserving linear operators
cites work: Representation of orthogonally additive polynomials
cites work: Q4971094
cites work: Polynomials on Riesz spaces
cites work: On \(n\)-disjoint operators
cites work: (p, r)-convex functions on vector lattices
cites work: Fremlin tensor products of concavifications of Banach lattices
cites work: Orthogonally additive polynomials on Dedekind \(\sigma\)-complete vector lattices
DOI: 10.15352/AOT.1807-1394
description: scientific article; zbMATH DE number 7009318