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
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.
PDF file (510 kB)
MSC: 46B04, 46B42, 47B65, 03C90, 03C98
A. G. Kusraev, “Injective Banach lattices: a survey”, Eurasian Math. J., 5:3 (2014), 58–79
Citation in format AMSBIB
\paper Injective Banach lattices: a survey
\jour Eurasian Math. J.
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This publication is cited in the following articles:
Kusraev A.G., Kutateladze S.S., “Some Applications of Boolean Valued Analysis”, J. Appl. Log.-IFCOLOG, 7:4 (2020), 427–457
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