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Vladikavkaz. Mat. Zh., 2012, Volume 14, Number 1, Pages 67–74 (Mi vmj411)  

This article is cited in 1 scientific paper (total in 2 paper)

Kantorovich's principle in action: $AW^*$-modules and injective Banach lattices

A. G. Kusraev

Southern Mathematical Institute, Vladikavkaz Science Center of the RAS, Vladikavkaz, Russia

Abstract: Making use of Boolean valued representation it is proved that Kaplansky–Hilbert lattices and injective Banach lattices may be produced from each other by means of the convexification procedure. The relationship between the Kantorovich's heuristic principle and the Boolean value transfer principle is also discussed.

Key words: Kantorovich's principle, Kaplansly–Hilbert module, injective Banach lattice, Boolean valued analysis, Boolean valued representation, Maharam operator, square of a vector lattice, convexification.

Full text: PDF file (180 kB)
References: PDF file   HTML file
UDC: 512.555+517.982
MSC: 06F25, 46A40
Received: 12.01.2012
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Citation: A. G. Kusraev, “Kantorovich's principle in action: $AW^*$-modules and injective Banach lattices”, Vladikavkaz. Mat. Zh., 14:1 (2012), 67–74

Citation in format AMSBIB
\Bibitem{Kus12}
\by A.~G.~Kusraev
\paper Kantorovich's principle in action: $AW^*$-modules and injective Banach lattices
\jour Vladikavkaz. Mat. Zh.
\yr 2012
\vol 14
\issue 1
\pages 67--74
\mathnet{http://mi.mathnet.ru/vmj411}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. K. Vodopyanov, E. I. Gordon, A. E. Gutman, A. V. Koptev, S. S. Kutateladze, S. A. Malyugin, Yu. G. Reshetnyak, “Anatoliyu Georgievichu Kusraevu — 60 let”, Sib. elektron. matem. izv., 10 (2013), 13–29  mathnet
    2. A. G. Kusraev, “Operators on injective Banach lattices”, Vladikavk. matem. zhurn., 18:1 (2016), 42–50  mathnet
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