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Matematicheskie Zametki, 2021, Volume 110, Issue 5, Pages 726–735
DOI: https://doi.org/10.4213/mzm13089
(Mi mzm13089)
 

This article is cited in 1 scientific paper (total in 1 paper)

Regularity of Continuous Multilinear Operators and Homogeneous Polynomials

Z. A. Kusraevaab

a Regional mathematical center of Southern Federal University, Rostov-on-Don
b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz
Full-text PDF (504 kB) Citations (1)
References:
Abstract: Regular multilinear operators and regular homogeneous polynomials acting between Banach lattices are automatically continuous, but the converse, in general, is not true. The problem arises of characterizing Banach lattices for which the classes of continuous and regular multilinear operators (or homogeneous polynomials) coincide. The aim of this note is to extend two results in this direction, earlier obtained for linear operators, to the above-mentioned classes of operators and polynomials. The main method is linearization with the use of the Fremlin tensor product of Banach lattices.
Keywords: Banach lattice, Levi property, multilinear operator, homogeneous polynomial, Fremlin tensor product, linearization.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation МК-4347.2021.1.1
Supported by a Presidential Program for State Support of Young Researchers–Candidates of Sciences (grant no. MK-4347.2021.1.1; agreeement no. 075-15-2021-407).
Received: 31.03.2021
Revised: 21.06.2021
English version:
Mathematical Notes, 2021, Volume 110, Issue 5, Pages 718–725
DOI: https://doi.org/10.1134/S0001434621110080
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: Z. A. Kusraeva, “Regularity of Continuous Multilinear Operators and Homogeneous Polynomials”, Mat. Zametki, 110:5 (2021), 726–735; Math. Notes, 110:5 (2021), 718–725
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm13089
  • https://doi.org/10.4213/mzm13089
  • https://www.mathnet.ru/eng/mzm/v110/i5/p726
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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