This article is cited in 1 paper

Kantorovich's principle in action: $AW^*$-modules and injective Banach lattices

A. G. Kusraev

Southern Mathematical Institute, Vladikavkaz Science Center of the RAS, Vladikavkaz, Russia

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.

Key words: Kantorovich's principle, Kaplansly–Hilbert module, injective Banach lattice, Boolean valued analysis, Boolean valued representation, Maharam operator, square of a vector lattice, convexification.

UDC: 512.555+517.982

MSC: 06F25, 46A40

Received: 12.01.2012

Language: English