Abelian von Neumann algebras, measure algebras and L^\infty-spaces

TL;DR

This paper explores the deep connections between abelian von Neumann algebras, measure algebras, and L^-spaces, providing new insights and an exposition of Maharam's theorem from the perspective of von Neumann algebras.

Contribution

It offers a novel account of the relationships among these mathematical structures, including a new perspective on Maharam's theorem within von Neumann algebra theory.

Findings

Clarifies the interplay between abelian von Neumann algebras and measure algebras

Provides an exposition of Maharam's theorem from the von Neumann algebra perspective

Enhances understanding of L^-spaces in relation to measure and operator algebras

Abstract

We give a fresh account of the astonishing interplay between abelian von Neumann algebras, L^\infty-spaces and measure algebras, including an exposition of Maharam's theorem from the von Neumann algebra perspective.