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Vladikavkaz. Mat. Zh., 2013, Volume 15, Number 3, Pages 54–57 (Mi vmj471)  

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

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.

Key words: vector lattice, universally complete vector lattice, $d$-basis, locally one-dimensional vector lattice, $\sigma$-distributivity, band preserving operator, strongly diagonal operator, band projection.

Full text: PDF file (124 kB)
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UDC: 517.98
Received: 25.07.2013

Citation: Z. A. Kusraeva, “Algebraic band preserving operators”, Vladikavkaz. Mat. Zh., 15:3 (2013), 54–57

Citation in format AMSBIB
\Bibitem{Kus13}
\by Z.~A.~Kusraeva
\paper Algebraic band preserving operators
\jour Vladikavkaz. Mat. Zh.
\yr 2013
\vol 15
\issue 3
\pages 54--57
\mathnet{http://mi.mathnet.ru/vmj471}


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    This publication is cited in the following articles:
    1. A. G. Kusraev, S. S. Kutateladze, “Boolean-valued analysis of order-bounded operators”, J. Math. Sci., 218:5 (2016), 609–635  mathnet  crossref  mathscinet
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