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Multiplicative representation of bilinear operators

A. G. Kusraev, S. N. Tabuev

Institute of Applied Mathematics and Informatics, Vladikavkaz Scientific Centre, RAS

Abstract: We establish that each lattice bimorphism from the Cartesian product of two vector lattices into a universally complete vector lattice is representable as the product of two lattice homomorphisms defined on the factors. This fact makes it possible to reduce the problem to the linear case and obtain some results on representation of an order bounded disjointness preserving bilinear operator as a strongly disjoint sum of weighted shift or multiplicative operators.

Keywords: order bounded bilinear operator, lattice bimorphism, weighted shift operator, multiplicative representation.

UDC: 517.98

Received: 23.10.2006
Revised: 03.07.2007

 English version: Siberian Mathematical Journal, 2008, 49:2, 287–294

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