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Eurasian Math. J., 2014, Volume 5, Number 3, Pages 58–79 (Mi emj164)  

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

Injective Banach lattices: a survey

A. G. Kusraevab

a North-Ossetian K.L. Khetagurov State University
b Southern Mathematical Institute, Vladikavkaz Science Center of the RAS, 22 Markus St., 362027 Vladikavkaz, Russia

Abstract: The work is aimed to survey recent results on injective Banach lattices, outline the Boolean-valued approach, and pose some open problems. The central idea of the investigation is the Boolean-valued transfer principle from $AL$-spaces to injective Banach lattices: Every injective Banach lattice is embedded into an appropriate Boolean-valued model, becoming an $AL$-space. To illustrate the method, a concrete description of injective Banach lattices similar to that of $AL$-spaces is presented and the isometric classification of injective Banach lattices is accomplished.

Keywords and phrases: $AL$-space, $AM$-space, injective Banach lattice, Boolean-valued model, Boolean-valued transfer principle, tensor product, homogeneous Banach lattice.

Full text: PDF file (510 kB)
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MSC: 46B04, 46B42, 47B65, 03C90, 03C98
Received: 23.05.2014
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Citation: A. G. Kusraev, “Injective Banach lattices: a survey”, Eurasian Math. J., 5:3 (2014), 58–79

Citation in format AMSBIB
\Bibitem{Kus14}
\by A.~G.~Kusraev
\paper Injective Banach lattices: a survey
\jour Eurasian Math. J.
\yr 2014
\vol 5
\issue 3
\pages 58--79
\mathnet{http://mi.mathnet.ru/emj164}


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    This publication is cited in the following articles:
    1. Kusraev A.G., Kutateladze S.S., “Some Applications of Boolean Valued Analysis”, J. Appl. Log.-IFCOLOG, 7:4 (2020), 427–457  mathscinet  isi
  • Eurasian Mathematical Journal
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