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This article is cited in 5 scientific papers (total in 5 papers)
Two applications of Boolean valued analysis
A. G. Kusraevab, S. S. Kutateladzec a Southern Mathematical Institute,
Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia
b North Ossetian State University, Vladikavkaz, Russia
c Sobolev Institute of Mathematics, Novosibirsk, Russia
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 $AL^p$ and $c_o(\Gamma)$ for the class of the so-called $\mathbb{B}$-cyclic Banach lattices, using the Boolean valued transfer for injective Banach lattices.
Keywords:
universally complete vector lattice, injective Banach lattice, $M$-projection, Maharam operator, $AL^p$-space, Boolean valued representation.
Received: 04.03.2019 Revised: 11.03.2019 Accepted: 12.03.2019
Citation:
A. G. Kusraev, S. S. Kutateladze, “Two applications of Boolean valued analysis”, Sibirsk. Mat. Zh., 60:5 (2019), 1153–1164; Siberian Math. J., 60:5 (2019), 902–910
Linking options:
https://www.mathnet.ru/eng/smj3139 https://www.mathnet.ru/eng/smj/v60/i5/p1153
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Abstract page: | 331 | Full-text PDF : | 90 | References: | 36 | First page: | 6 |
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