Poisson boundaries of II<sub>1</sub> factors
نویسندگان
چکیده
We introduce Poisson boundaries of II $_1$ factors with respect to density operators that give the traces. The boundary is a von Neumann algebra contains factor and particular example unital completely positive map as introduced by Izumi. Studying inclusion into its boundary, we develop number notions, such double ergodicity entropy, can be seen natural analogues results regarding Furstenberg. use techniques developed answer problem Popa showing all finite satisfy his MV property. also extend result Nevo property (T) rise an entropy gap.
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2022
ISSN: ['0010-437X', '1570-5846']
DOI: https://doi.org/10.1112/s0010437x22007539