Given an inclusion $N\subset M$ of $\rm{II}_{1}$ factors with trivial relative commutant, this paper lists all operators $x,y\in M$ such that the left $N$-module generated by $x$ is equal to or contained in the right $N$-module generated by $y$.
References
J. Fang, R.R. Smith, S.A. White and A.D. Wiggins, Groupoid normalizers of tensor products, J. Funct. Anal. 258 (2011), no. 1, 20–49. MR2557953 1192.46055 10.1016/j.jfa.2009.10.005 J. Fang, R.R. Smith, S.A. White and A.D. Wiggins, Groupoid normalizers of tensor products, J. Funct. Anal. 258 (2011), no. 1, 20–49. MR2557953 1192.46055 10.1016/j.jfa.2009.10.005
K. Mukherjee, Masas and Bimodule Decompositions of $\rm{II}_{1}$ Factors, Q. J. Math. 62 (2011), no. 2, 451–486. MR2805213 1222.46047 10.1093/qmath/hap038 K. Mukherjee, Masas and Bimodule Decompositions of $\rm{II}_{1}$ Factors, Q. J. Math. 62 (2011), no. 2, 451–486. MR2805213 1222.46047 10.1093/qmath/hap038
A.M. Sinclair and R.R. Smith, Finite von Neumann algebras and masas, volume 351 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 2008. MR2433341 1154.46035 A.M. Sinclair and R.R. Smith, Finite von Neumann algebras and masas, volume 351 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 2008. MR2433341 1154.46035
