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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