Two Applications of Boolean Valued Analysis

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 c₀ (Γ) for the class of the so-called \(\mathbb{B}\)-cyclic Banach lattices, using the Boolean valued transfer for injective Banach lattices.