{"title":"Extremal structure of cones of positive homogeneous polynomials. Part II","authors":"Zalina A. Kusraeva","doi":"10.1016/j.jmaa.2025.129409","DOIUrl":null,"url":null,"abstract":"<div><div>The necessary and sufficient conditions under which the cone of positive homogeneous polynomials between vector lattices coincides with the closed convex hull of the set of sums of monomials in lattice homomorphisms are found. Incidentally the answer for the following question is established: when the cone of positive multilinear operators between vector lattices serves as a point-wise uniformly closed convex hull of the set of lattice multimorphisms.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 2","pages":"Article 129409"},"PeriodicalIF":1.2000,"publicationDate":"2025-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X25001908","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/2/25 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
The necessary and sufficient conditions under which the cone of positive homogeneous polynomials between vector lattices coincides with the closed convex hull of the set of sums of monomials in lattice homomorphisms are found. Incidentally the answer for the following question is established: when the cone of positive multilinear operators between vector lattices serves as a point-wise uniformly closed convex hull of the set of lattice multimorphisms.
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The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
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