Document Zbl 1326.46018

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Kusraev, A. G.

Kantorovich’s principle in action: \(AW^\ast\)-modules and injective Banach lattices. (English) Zbl 1326.46018

Vladikavkaz. Mat. Zh. 14, No. 1, 67-74 (2012).

Summary: 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.

Cited in 2 Documents

MSC:

46B42	Banach lattices
06F30	Ordered topological structures
46A40	Ordered topological linear spaces, vector lattices

Keywords:

Kantorovich’s principle; Kaplansky-Hilbert module; injective Banach lattice; Boolean valued analysis; Boolean valued representation; Maharam operator; square of a vector lattice; convexification

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