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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 5, Pages 1153–1164
DOI: https://doi.org/10.33048/smzh.2019.60.512
(Mi smj3139)
 

This article is cited in 5 scientific papers (total in 5 papers)

Two applications of Boolean valued analysis

A. G. Kusraevab, S. S. Kutateladzec

a Southern Mathematical Institute, Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia
b North Ossetian State University, Vladikavkaz, Russia
c Sobolev Institute of Mathematics, Novosibirsk, Russia
Full-text PDF (534 kB) Citations (5)
References:
Abstract: The paper contains two main results that are obtained by using Boolean valued analysis. The first asserts that a universally complete vector lattice without locally one-dimensional bands can be decomposed into a direct sum of two vector sublattices that are laterally complete and invariant under all band projections and there exists a band preserving linear isomorphism of each of these sublattices onto the original lattice. The second result establishes a counterpart of the Ando Theorem on the joint characterization of $AL^p$ and $c_o(\Gamma)$ for the class of the so-called $\mathbb{B}$-cyclic Banach lattices, using the Boolean valued transfer for injective Banach lattices.
Keywords: universally complete vector lattice, injective Banach lattice, $M$-projection, Maharam operator, $AL^p$-space, Boolean valued representation.
Funding agency Grant number
Siberian Branch of Russian Academy of Sciences I.1.2, проект № 0314-2019-0005
The authors were supported by the Program of Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences (Grant No. I.1.2, Project 0314–2019–0005).
Received: 04.03.2019
Revised: 11.03.2019
Accepted: 12.03.2019
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 5, Pages 902–910
DOI: https://doi.org/10.1134/S0037446619050124
Bibliographic databases:
Document Type: Article
UDC: 517.11+517.98
Language: Russian
Citation: A. G. Kusraev, S. S. Kutateladze, “Two applications of Boolean valued analysis”, Sibirsk. Mat. Zh., 60:5 (2019), 1153–1164; Siberian Math. J., 60:5 (2019), 902–910
Citation in format AMSBIB
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\paper Two applications of Boolean valued analysis
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\pages 1153--1164
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\crossref{https://doi.org/10.33048/smzh.2019.60.512}
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\transl
\jour Siberian Math. J.
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\issue 5
\pages 902--910
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  • https://www.mathnet.ru/eng/smj/v60/i5/p1153
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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