Full factors, bicentralizer flow and approximately inner automorphisms

• 成果类型: Article
• 署名作者: Marrakchi, Amine
• 署名单位: Ecole Normale Superieure de Lyon (ENS de LYON)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-00971-w
• 发表日期: 2020
• 页码: 375-398
• 关键词: OPERATOR-VALUED WEIGHTS

摘要

We show that a factor M is full if and only if the C*-algebra generated by its left and right regular representations contains the compact operators. We prove that the bicentralizer flow of a type III1 factor is always ergodic. As a consequence, for any type III1 factor M and any lambda is an element of]0, 1], there exists an irreducible AFD type III lambda subfactor with expectation in M. Moreover, any type III1 factor M which satisfies M congruent to M (circle times) over bar R-lambda for some lambda is an element of]0, 1[ has trivial bicentralizer. Finally, we give a counter-example to the characterization of approximately inner automorphisms conjectured by Connes and we prove a weaker version of this conjecture. In particular, we obtain a new proof of Kawahigashi-Sutherland-Takesaki's result that every automorphism of the AFD type III1 factor is approximately inner.