This paper is concerned with the commutant of unbounded operators affiliated with finite von Neumann algebras. We prove an unbounded Fuglede–Putnam type theorem and present examples of closed ...

Consider the ℬ-valued probability space (𝒜,E,ℬ), where 𝒜 is a tracial von Neumann algebra. We extend the theory of operator-valued free probability to the algebra of affiliated operators 𝒜̃. For a ...