@misc{AnantharamanPopa,
  author = {Anantharaman, Claire and Popa, Sorin},
  title = {An introduction to {$\mathrm{II}_1$} factors},
  howpublished = {Draft monograph},
  note = {Author-hosted version IIunV15; accessed September 23, 2026.},
  url = {https://www.math.ucla.edu/~popa/Books/IIunV15.pdf}
}

@article{Edwards1978,
  author = {Edwards, David Albert},
  title = {On the existence of probability measures with given marginals},
  journal = {Annales de l'Institut Fourier},
  volume = {28},
  number = {4},
  year = {1978},
  pages = {53--78},
  doi = {10.5802/aif.717},
  url = {https://www.numdam.org/article/AIF_1978__28_4_53_0.pdf}
}

@article{Strassen1965,
  author = {Strassen, Volker},
  title = {The existence of probability measures with given marginals},
  journal = {The Annals of Mathematical Statistics},
  volume = {36},
  number = {2},
  year = {1965},
  pages = {423--439},
  doi = {10.1214/aoms/1177700153}
}

@article{Tucci2008,
  author = {Tucci, Gabriel H.},
  title = {Some quasinilpotent generators of the hyperfinite {$\mathrm{II}_1$} factor},
  journal = {Journal of Functional Analysis},
  volume = {254},
  number = {12},
  year = {2008},
  pages = {2969--2994},
  doi = {10.1016/j.jfa.2008.03.012}
}

@article{zfs,
  author = {Zhu, Zhangsheng and Fang, Junsheng and Shi, Rui},
  title = {On a class of operators in the hyperfinite {II}$_1$ factor},
  journal = {Mathematica Scandinavica},
  volume = {120},
  number = {2},
  pages = {249--271},
  year = {2017},
  doi = {10.7146/math.scand.a-25625},
  url = {https://journals.msp.org/mscand/article/view/322}
}

@article{fuglede-kadison,
  author = {Fuglede, Bent and Kadison, Richard V.},
  title = {Determinant theory in finite factors},
  journal = {Annals of Mathematics. Second Series},
  volume = {55},
  number = {3},
  pages = {520--530},
  year = {1952},
  doi = {10.2307/1969645}
}

@incollection{brown,
  author = {Brown, Lawrence G.},
  title = {Lidski{\u\i}'s theorem in the type {II} case},
  booktitle = {Geometric Methods in Operator Algebras (Kyoto, 1983)},
  series = {Pitman Research Notes in Mathematics Series},
  volume = {123},
  pages = {1--35},
  publisher = {Longman Scientific and Technical},
  address = {Harlow},
  year = {1986}
}

@article{haagerup-schultz,
  author = {Haagerup, Uffe and Schultz, Hanne},
  title = {Invariant subspaces for operators in a general {II}$_1$-factor},
  journal = {Publications Math{\'e}matiques de l'IH{\'E}S},
  volume = {109},
  pages = {19--111},
  year = {2009},
  doi = {10.1007/s10240-009-0018-7}
}

@article{dykema-schultz,
  author = {Dykema, Ken and Schultz, Hanne},
  title = {Brown measure and iterates of the {Aluthge} transform for some operators arising from measurable actions},
  journal = {Transactions of the American Mathematical Society},
  volume = {361},
  number = {12},
  pages = {6583--6593},
  year = {2009},
  doi = {10.1090/S0002-9947-09-04762-X},
  eprint = {math/0512197},
  archivePrefix = {arXiv}
}

@article{mori,
  author = {Mori, Michiya},
  title = {Lattice isomorphisms between projection lattices of von {Neumann} algebras},
  journal = {Forum of Mathematics, Sigma},
  volume = {8},
  pages = {e49},
  year = {2020},
  doi = {10.1017/fms.2020.53},
  note = {19~pp.}
}

@article{dykema-haagerup,
  author = {Dykema, Ken and Haagerup, Uffe},
  title = {Invariant subspaces of the quasinilpotent {DT}-operator},
  journal = {Journal of Functional Analysis},
  volume = {209},
  number = {2},
  pages = {332--366},
  year = {2004},
  doi = {10.1016/S0022-1236(03)00167-8}
}

@article{dykema2005,
  author = {Dykema, Ken},
  title = {Hyperinvariant subspaces for some {$B$}-circular operators},
  journal = {Mathematische Annalen},
  volume = {333},
  number = {3},
  pages = {485--523},
  year = {2005},
  doi = {10.1007/s00208-005-0669-8},
  note = {With an appendix by Gabriel Tucci}
}

@article{cho-ko-lee,
  author = {Ch\={o}, Muneo and Ko, Eungil and Lee, Ji Eun},
  title = {{$(\infty,C)$}-isometric operators},
  journal = {Operators and Matrices},
  volume = {11},
  number = {3},
  pages = {793--806},
  year = {2017},
  doi = {10.7153/oam-11-56}
}

@misc{direct-companion,
  author = {{OpenAI}},
  title = {{Backward intertwiners and a transitive commutant}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Backward-intertwiners-and-a-transitive-commutant-September-27-2026/paper.pdf}{OAI:Backward-intertwiners-and-a-transitive-commutant-September-27-2026}},
  year = {2026}
}
