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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
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.
Received: 31.03.2021 Revised: 21.06.2021
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
Linking options:
https://www.mathnet.ru/eng/mzm13089https://doi.org/10.4213/mzm13089 https://www.mathnet.ru/eng/mzm/v110/i5/p726
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Abstract page: | 241 | Full-text PDF : | 29 | References: | 41 | First page: | 9 |
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