On a Question of Kaplansky Concerning his Density Theorem

C. R. Math. Rep. Acad. Sci. Canada Vol. 46 (4) 2024, pp. 117–118
(Received: 2024-08-29 )

George A. Elliott, FRSC, Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4; e-mail: elliott@math.toronto.edu

Charles J. K. Griffin, Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4, e-mail: charlie.griffin@mail.utoronto.ca

Abstract/Résumé:

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.

Une nouvelle démonstration, suivant une suggestion de Kaplansky, d’utiliser un résultat de Dixmier, et dans cette façon d’éviter les familles d’opérateurs non bornées, est donnée du théorème de densité de Kaplansky.

Keywords:

AMS Subject Classification: General theory of $C^*$-algebras, General theory of von Neumann algebras 46L05, 46L10

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