Measurable operators in a Boolean-valued model of set theory. (Russian) Zbl 0704.46044
Summary: A connection between the ring of operators, associated to a von Neumann algebra and measurable with respect to a centre-valued trace, and the ring of operators, measurable with respect to a scalar trace is established in a Boolean valued model of set theory. An application to the construction of the integral for centre-valued traces is given.
MSC:
46L51 | Noncommutative measure and integration |
46L53 | Noncommutative probability and statistics |
46L54 | Free probability and free operator algebras |
46S20 | Nonstandard functional analysis |
03C90 | Nonclassical models (Boolean-valued, sheaf, etc.) |