Geometric Description of the Preduals of Atomic Commutative von Neumann Algebras

TL;DR

This paper characterizes the geometric structure of the predual spaces of atomic commutative von Neumann algebras using the framework of strongly facially symmetric spaces.

Contribution

It provides a geometric description of the preduals of atomic commutative von Neumann algebras, linking operator algebra theory with geometric analysis.

Findings

Preduals are strongly facially symmetric spaces.

Characterization of these spaces in geometric terms.

Connection between algebraic and geometric properties.

Abstract

Strongly facially symmetric spaces isometrically isomorphic to the predual space of an atomic commutative von Neumann algebra are described