A note on faithful traces on a von Neumann algebra

TL;DR

This paper presents techniques for constructing faithful traces on von Neumann algebras from existing families of semifinite or finite traces, enhancing the understanding of trace properties in operator algebras.

Contribution

It introduces methods to generate faithful traces from sufficient families of existing traces on von Neumann algebras, providing new tools for operator algebra analysis.

Findings

New techniques for constructing faithful traces

Applicable to semifinite and finite traces

Improves trace analysis in von Neumann algebras

Abstract

In this short note we give some techniques for constructing, starting from a {\it sufficient} family $\mc F$ of semifinite or finite traces on a von Neumann algebra $\M$, a new trace which is faithful.