A note on injective factors with trivial bicentralizer

Abstract

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.

arXiv commentThe paper will appear in the Publications of Research Institute for Mathematical Sciences, Kyoto University