# 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

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