Two Applications of Boolean Valued Analysis
- 作者: Kusraev A.G.1, Kutateladze S.S.2
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隶属关系:
- Southern Mathematical Institute, Vladikavkaz Scientific Center of the Russian Academy of Sciences
- Sobolev Institute of Mathematics
- 期: 卷 60, 编号 5 (2019)
- 页面: 902-910
- 栏目: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172673
- DOI: https://doi.org/10.1134/S0037446619050124
- ID: 172673
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详细
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.
作者简介
A. Kusraev
Southern Mathematical Institute, Vladikavkaz Scientific Center of the Russian Academy of Sciences
编辑信件的主要联系方式.
Email: kusraev@smath.ru
俄罗斯联邦, Vladikavkaz
S. Kutateladze
Sobolev Institute of Mathematics
编辑信件的主要联系方式.
Email: sskut@math.nsc.ru
俄罗斯联邦, Novosibirsk
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