Abstract
The paper contains two main results that are obtained by using Boolean valued analysis. The first asserts that a universally complete vector lattice without locally one-dimensional bands can be decomposed into a direct sum of two vector sublattices that are laterally complete and invariant under all band projections and there exists a band preserving linear isomorphism of each of these sublattices onto the original lattice. The second result establishes a counterpart of the Ando Theorem on the joint characterization of ALp and c0 (Γ) for the class of the so-called \(\mathbb{B}\)-cyclic Banach lattices, using the Boolean valued transfer for injective Banach lattices.
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To Yu. G. Reshetnyak on the occasion of his 90th birthday.
Russian Text © The Author(s), 2019, published in Sibirskii Matematicheskii Zhurnal, 2019, Vol. 60, No. 5, pp. 1153–1164.
The authors were supported by the Program of Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences (Grant No. I.1.2, Project 0314-2019-0005).
The authors express their gratitude to the referee for removing numerous typos and inaccuracies.
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Kusraev, A.G., Kutateladze, S.S. Two Applications of Boolean Valued Analysis. Sib Math J 60, 902–910 (2019). https://doi.org/10.1134/S0037446619050124
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DOI: https://doi.org/10.1134/S0037446619050124