Algebraic band preserving operators

Kusraeva, Z. A.
Vladikavkaz Mathematical Journal 2013. Vol. 15. Issue 3.

Abstract:
It is shown that for a universally complete vector lattice \(E\) the following are equivalent: (1) the Boolean algebra of band projections \(\mathbb{P}(E)\) is \(\sigma\)-distributive; (2) every algebraic band preserving operator in \(E\) is strongly diagonal; (3) every band preserving projection in \(E\) is a band projection.

Keywords: Vector lattice, universally complete vector lattice, \(d\)-basis, locally one-dimensional vector lattice, \(\sigma\)-distributivity, band preserving operator, strongly diagonal operator, band projection

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