This article is cited in 3 papers

On order bounded disjointness preserving operators

A. G. Kusraev^ab, S. S. Kutateladze<sup>c

a</sup> North Ossetian State University, Vladikavkaz, Russia
^b Southern Mathematical Institute, Vladikavkaz Science Center of the Russian Academy of Sciences, Vladikavkaz, Russia
^c Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: The paper is aimed at demonstrating that some properties of order bounded operators in vector lattices are just Boolean valued interpretations of elementary properties of order bounded functionals. We present the general machinery and illustrate it with a few new results on order bounded disjointness preserving and $n$-disjoint operators.

Keywords: Boolean valued analysis, vector lattice, disjointness preserving operator, lattice homomorphism.

UDC: 517.98

Received: 19.06.2014

 English version: Siberian Mathematical Journal, 2014, 55:5, 915–928

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