# Two Applications of Boolean Valued Analysis

## TL;DR

This paper applies Boolean valued analysis to decompose certain vector lattices and characterizes cyclic Banach lattices, providing new structural insights and transfer principles in functional analysis.

## Contribution

It introduces a novel decomposition of universally complete vector lattices and extends the Ando Theorem to cyclic Banach lattices via Boolean valued transfer.

## Key findings

- Decomposition of vector lattices into invariant sublattices
- Extension of Ando Theorem to cyclic Banach lattices
- Application of Boolean valued analysis to Banach lattice theory

## 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.

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Source: https://tomesphere.com/paper/1908.02471