On a question of Kaplansky concerning his density theorem

TL;DR

This paper presents a new proof of Kaplansky's density theorem, utilizing Dixmier's result to simplify the proof and avoid the use of unbounded nets of operators.

Contribution

It introduces a novel proof of Kaplansky's density theorem based on Dixmier's result, simplifying the original argument.

Findings

New proof of Kaplansky's density theorem

Avoids unbounded nets of operators

Utilizes a result of Dixmier

Abstract

A new proof following a suggestion of Kaplansky to use a result of Dixmier, and in this way avoid unbounded nets of operators, is given of the Kaplansky density theorem.