Kantorovich's principle in action: \(AW^\ast\)-modules and Injective Banach lattices

Kusraev A. G.
Vladikavkaz Mathematical Journal 2012. Vol. 14. Issue 1.

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.

Keywords: Kantorovich's principle, Kaplansly--Hilbert module, injective Banach lattice, Boolean valued analysis, Boolean valued representation, Maharam operator, square of a vector lattice, convexification

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