Boolean Methods in the Theory of Vector Lattices

从序收敛角度看布尔代数与向量格的原子性

Atomicity of Boolean algebras and vector lattices in terms of order convergence

本研究围绕布尔代数与阿基米德向量格的原子性展开，分别证明了布尔代数序收敛为紧收敛空间、向量格序区间序收敛紧、向量格uo收敛由拓扑诱导的充要条件均与完备性和原子性相关。

Two Applications of Boolean Valued Analysis

The paper contains two main results that are obtained by 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 to the original lattice. The second result establishes a counterpart of the Ando Theorem on the joint characterization of $A\!L^p$ and $c_0$ for the class of cyclic Banach lattices, using the Boolean value…

Some Aspects of Boolean Valued Analysis

This is a survey of some recent applications of Boolean valued analysis to operator theory and harmonic analysis. Under consideration are pseudoembedding operators, the noncommutative Wickstead problem, the Radon-Nikodym Theorem for JB-algebras, and the Bochner Theorem for lattice-valued positive definite mappings on locally compact groups.

Boolean Valued Analysis of Order Bounded Operators

This is a survey of some recent applications of Boolean valued models of set theory to order bounded operators in vector lattices.

Unital hyperarchimedean vector lattices

We prove that the category of unital hyperarchimedean vector lattices is equivalent to the category of Boolean algebras. The key result needed to establish the equivalence is that, via the Yosida representation, such a vector lattice is naturally isomorphic to the vector lattice of all locally constant real-valued continuous functions on a Boolean (=compact Hausdorff totally disconnected) space. We give two applications of our main result.