This article is cited in 1 scientific paper (total in 1 paper)
Algebraic band preserving operators
Z. A. Kusraeva
South Mathematical Institute of VSC RAS, Vladikavkaz, Russia
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.
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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Z. A. Kusraeva, “Algebraic band preserving operators”, Vladikavkaz. Mat. Zh., 15:3 (2013), 54–57
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\paper Algebraic band preserving operators
\jour Vladikavkaz. Mat. Zh.
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A. G. Kusraev, S. S. Kutateladze, “Boolean-valued analysis of order-bounded operators”, J. Math. Sci., 218:5 (2016), 609–635
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