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Eurasian Mathematical Journal, 2014, том 5, номер 3, страницы 58–79
(Mi emj164)
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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
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
Аннотация:
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.
Ключевые слова и фразы:
$AL$-space, $AM$-space, injective Banach lattice, Boolean-valued model, Boolean-valued transfer principle, tensor product, homogeneous Banach lattice.
Поступила в редакцию: 23.05.2014
Образец цитирования:
A. G. Kusraev, “Injective Banach lattices: a survey”, Eurasian Math. J., 5:3 (2014), 58–79
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj164 https://www.mathnet.ru/rus/emj/v5/i3/p58
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Страница аннотации: | 357 | PDF полного текста: | 164 | Список литературы: | 43 |
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