C*-algebras where every element is a limit of products of positive elements

TL;DR

This paper characterizes unital C*-algebras in which every element can be approximated by products of positive elements, providing an answer to a previously open question.

Contribution

It offers a complete characterization of such C*-algebras, advancing understanding of their structure and properties.

Findings

Identifies conditions under which every element is a limit of products of positive elements

Answers a question posed by Murphy and Phillips

Enhances the theoretical framework of C*-algebra structure

Abstract

We obtain a characterization of the unital C*-algebras with the property that every element is a limit of products of positive elements, thereby answering a question of Murphy and Phillips.