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Tensor Products of Archimedean Riesz Spaces: a Representational Approach

Anthony W. Wickstead

Abstract

A representational approach to constructing the Fremlin tensor product of two Archimedean Riesz spaces. [Warning: do not view the HTML version!]

Tensor Products of Archimedean Riesz Spaces: a Representational Approach

Abstract

A representational approach to constructing the Fremlin tensor product of two Archimedean Riesz spaces. [Warning: do not view the HTML version!]
Paper Structure (3 sections, 11 theorems, 3 equations)

This paper contains 3 sections, 11 theorems, 3 equations.

Table of Contents

  1. Introduction
  2. The starting point
  3. Uniqueness and properties

Key Result

Theorem 3.1

Let $X, Y$ and $Z$ be compact Hausdorff spaces, and let $E\subseteq C(X)$ and $F\subseteq C(Y)$ be supremum norm dense Riesz subspaces containing the constants. Let $\phi:E\times F\to C(Z)$ be a Riesz bimorphism then it can be factored as where $\chi$ is the natural bilinear embedding and $T$ is a lattice homomorphism which is uniquely determined by $\phi$.

Theorems & Definitions (21)

  • Theorem 3.1
  • proof
  • Lemma 3.2
  • proof
  • Proposition 3.3
  • proof
  • Theorem 3.4
  • proof
  • Corollary 3.5
  • proof
  • ...and 11 more