On the sequential monotone closure of $CD_{\omega}(K)$ spaces

TL;DR

This paper addresses a problem in the theory of Banach lattices related to the sequential monotone closure of certain spaces, providing a resolution to a question posed by Wickstead.

Contribution

It solves a specific open problem about the sequential monotone closure of $CD_{oldsymbol{ extomega}}(K)$ spaces, advancing the understanding of Riesz completions in Banach lattice theory.

Findings

Resolved Wickstead's problem on sequential monotone closure.

Clarified properties of Riesz completion of regular operator spaces.

Contributed to the theory of Banach lattices and their completions.

Abstract

In this short note, we settle a problem posed by Wickstead in ~\cite{W:24}, arising from the study of the Riesz completion of spaces of regular operators between Banach lattices.