Pseudo-Diagonals and Uniqueness Theorems

TL;DR

This paper explores a special class of abelian C*-subalgebras called pseudo-diagonals, providing a unified framework for two important uniqueness theorems in graph C*-algebras and reduced crossed products.

Contribution

It introduces the concept of pseudo-diagonals to unify and extend the understanding of uniqueness theorems in different classes of C*-algebras.

Findings

Unified treatment of uniqueness theorems for graph C*-algebras and reduced crossed products

Identification of pseudo-diagonals as key structural elements

Enhanced understanding of abelian subalgebras in C*-algebra theory

Abstract

We examine a certain type of abelian C*-subalgebras that allow one to give a unified treatment of two uniqueness theorems: for graph C*-algebras and for certain reduced crossed products.