This article is cited in 8 papers

The Boolean transfer principle for injective Banach lattices

A. G. Kusraev<sup>ab

a</sup> 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.

UDC: 517.11+517.98

Received: 26.09.2014

DOI: 10.17377/smzh.2015.56.511

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

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