Two Applications of Boolean Valued Analysis

Abstract

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 valued transfer for injective Banach lattices.

This a preprint of the work accepted for publication in Siberian Mathematical Journal; $\text{c◯}$ 2019, Pleiades Publishing Ltd. http://pleiades.online/