A note on injective factors with trivial bicentralizer

A note on injective factors with trivial bicentralizer

We give an alternative proof that an injective factor on a Hilbert space with trivial bicentralizer is ITPFI. Our proof is given in parallel with each type of factors and it is based on the strategy of Haagerup. As a consequence, the uniqueness theorem of injective factors except type III\(_0\) foll...

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Veröffentlicht in:arXiv.org 2023-10
1. Verfasser: Okayasu, Rui
Format: Artikel
Sprache:eng
Schlagworte:
Hilbert space
Uniqueness theorems
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Zusammenfassung:We give an alternative proof that an injective factor on a Hilbert space with trivial bicentralizer is ITPFI. Our proof is given in parallel with each type of factors and it is based on the strategy of Haagerup. As a consequence, the uniqueness theorem of injective factors except type III\(_0\) follows from Araki-Woods' result.
ISSN:2331-8422