# Ando-Choi-Effros liftings for regular maps between Banach lattices

## TL;DR

This paper extends the Ando-Choi-Effros lifting theorem to regular maps between Banach lattices, incorporating order structure considerations to establish new lifting conditions.

## Contribution

It introduces two versions of the lifting theorem for regular maps between Banach lattices, accounting for their order structure, which is a novel extension.

## Key findings

- Established lifting conditions for regular maps in Banach lattices
- Extended classical theorems to include order structure considerations
- Provided two versions of the lifting theorem

## Abstract

The Ando-Choi-Effros lifting theorem provides conditions under which a bounded linear mapping taking values in a quotient space can be lifted through the quotient map. We prove two versions of said theorem for regular maps between Banach lattices. Our conditions mirror the classical ones, but additionally taking into account the order structure.