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Sibirsk. Mat. Zh., 2015, Volume 56, Number 5, Pages 1111–1129 (Mi smj2701)  

This article is cited in 3 scientific papers (total in 3 papers)

The Boolean transfer principle for injective Banach lattices

A. G. Kusraevab

a North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz, Russia
b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia

Abstract: The aim of this paper is to apply the approach of Boolean-valued analysis to the theory of injective Banach lattices and to establish the Boolean-valued transfer principle from $AL$-spaces to injective Banach lattices. We prove that each injective Banach lattice embeds into an appropriate Boolean-valued model, becoming an $AL$-space. Hence, each theorem about an $AL$-space within Zermelo–Fraenkel set theory has an analog in the original injective Banach lattice interpreted as a Boolean-valued $AL$-space. Translation of theorems from $AL$-spaces to injective Banach lattices is carried out by the appropriate general operations of Boolean-valued analysis.

Keywords: injective Banach lattice, $AL$-space, splitting property, $M$-projection, Maharam operator, Boolean-valued representation, descent, ascent.

DOI: https://doi.org/10.17377/smzh.2015.56.511

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English version:
Siberian Mathematical Journal, 2015, 56:5, 888–900

Bibliographic databases:

UDC: 517.11+517.98
Received: 26.09.2014

Citation: A. G. Kusraev, “The Boolean transfer principle for injective Banach lattices”, Sibirsk. Mat. Zh., 56:5 (2015), 1111–1129; Siberian Math. J., 56:5 (2015), 888–900

Citation in format AMSBIB
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\paper The Boolean transfer principle for injective Banach lattices
\jour Sibirsk. Mat. Zh.
\yr 2015
\vol 56
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\pages 1111--1129
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\issue 5
\pages 888--900
\crossref{https://doi.org/10.1134/S0037446615050110}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. G. Kusraev, “Atomicity in injective Banach lattices”, Vladikavk. matem. zhurn., 17:3 (2015), 44–52  mathnet
    2. A. G. Kusraev, “Operators on injective Banach lattices”, Vladikavk. matem. zhurn., 18:1 (2016), 42–50  mathnet
    3. A. G. Kusraev, B. B. Tasoev, “Integrirovanie po polozhitelnoi mere so znacheniyami v kvazibanakhovoi reshetke”, Vladikavk. matem. zhurn., 20:1 (2018), 69–85  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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