A note on commutators in algebras of unbounded operators

A note on commutators in algebras of unbounded operators

We show that the identity is the sum of two commutators in the algebra of all operators affiliated with a von Neumann algebra of type II1, settling a question, in the negative, that had puzzled a number of us.

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Veröffentlicht in:Expositiones mathematicae 2020-06, Vol.38 (2), p.232-239
Hauptverfasser: Kadison, Richard V., Liu, Zhe, Thom, Andreas
Format: Artikel
Sprache:eng
Schlagworte:
Commutators
Mathematics
Physical Sciences
Rings of operators
Science & Technology
von Neumann algebras
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Beschreibung
Zusammenfassung:We show that the identity is the sum of two commutators in the algebra of all operators affiliated with a von Neumann algebra of type II1, settling a question, in the negative, that had puzzled a number of us.
ISSN:0723-0869
1878-0792
DOI:10.1016/j.exmath.2020.01.004