# Journal of Operator Theory

Volume 75, Issue 1, Winter 2016  pp. 209-223.

Relative commutant of an unbounded operator affiliated with a finite von Neumann algebra

Authors:  Don Hadwin (1), Junhao Shen (2), Wenming Wu (3) and Wei Yuan (4)
Author institution: (1) Mathematics Department, University of New Hampshire, Durham, NH 03824, U.S.A.
(2) Mathematics Department, University of New Hampshire, Durham, NH 03824, U.S.A.
(3)School of Mathematical Science, Chongqing Normal University, Chongqing, 401331, China
(4) Academy of Mathematics and System Science, Chinese Academy of Science, Beijing, 100084, China

Summary: 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 operators affiliated with some $\mathrm{II}_1$ factor with trivial relative commutant in the factor.

DOI: http://dx.doi.org/10.7900/jot.2015jan23.2065
Keywords: Fuglede-Putnam theorem, $\mathrm{II}_1$ factors, unbounded operators, relative commutant, transitive lattice