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On the sequential monotone closure of $CD_ω(K)$ spaces

Sukrit Chalana, Denny H. Leung, Foivos Xanthos

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.

On the sequential monotone closure of $CD_ω(K)$ spaces

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.
Paper Structure (2 sections, 9 theorems, 17 equations)

This paper contains 2 sections, 9 theorems, 17 equations.

Table of Contents

  1. Introduction
  2. The main result

Key Result

Proposition 2.1

Let $K$ be a perfect Baire space, then the space $CD_\omega(K)$ is an order dense, majorizing and closed sublattice of $(B(K),||\cdot||_\infty)$. Moreover, there exists a bounded linear projection $P_c: CD_\omega(K) \rightarrow C_b(K)$ that is also a lattice homomorphism such that $[P_c(f) \neq f]$

Theorems & Definitions (20)

  • Definition 1.1
  • Proposition 2.1
  • proof
  • Lemma 2.2
  • proof
  • Theorem 2.3
  • proof
  • Proposition 2.4
  • proof
  • Theorem 2.5
  • ...and 10 more