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яндекс.ћетрика

DOI: 10.23671/VNC.2014.3.7352

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
Language: Russian Download the full text  
For citation: Kusraeva Z. A. Algebraic band preserving operators. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 15, no. 3, pp.54-57. DOI 10.23671/VNC.2014.3.7352


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