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Copyright © 2023 L.W. Marcoux, Esq.
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Page last updated: August 16, 2023.

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He gazed up at the enormous face. Forty years it had taken him to learn what kind of smile was hidden beneath the dark moustache. O cruel, needless misunderstanding! O stubborn, self-willed exile from the loving breast! Two gin-scented tears trickled down the sides of his nose. But it was all right, everything was all right, the struggle was finished. He had won the victory over himself. He loved Big Brother.

George Orwell: 1984

Things I do

    A bunch of research.

    I teach a bunch of math and pure math courses.

    I supervise graduate students.

    I serve on a bunch of committees.

Teaching testimonials

It's all fun and games until u have him in a fourth yr analysis course :'(


Any course with Laurent Marcoux is like a Final Destination film. Be careful of where you sit on the first day of class.


Taking a class with him will make you a better person, so I highly recommend it.


(expletive deleted) I just noticed that Marcoux is going to teach PMATH450 this winter, but I have to take it since it's my last term...


(same expletive as above deleted) I just saw that Marcoux is teaching 453 this fall and I have heard a lot of bad stories about him before. Would anybody like to share your experience with him?---- response: I took 453 with Marcoux and it was my favourite course of all time. He is a fantastic instructor and gives very nice (hard) assignments.


His innuendos kept me focused.

2017 - Math 147

The course contains a lot of propositions that sound like they should be true, but aren't (or maybe I just lost track, and they actually are true? I dunno).

2016 - Math 148

Persists admirably at making dry jokes despite the near total absence of student encouragement.

2012 - PMath 334

Very good at math for a guy raised by chickens.

2012 - Math 228

No comment.

2002 - Math 247
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My general field of interest is Operator Theory and Operator Algebras. In particular I am interested in the approximation and structure of linear operators acting on a Hilbert space, as well as the study of non-selfadjoint and selfadjoint operator algebras. I have also dabbled in problems of interest to Linear Algebraists.

Currently my interests include: similarity of operator algebras to C*-algebras, quasidiagonality of operators and of operator algebras, consequences of the total reduction property for operator algebras, and characterising (the closures of) the set of commutators of different families of operators in B(H) and in operator algebras. At some point, through no fault of my own, I may utter the phrase "mixed unitary quantum channel", but if I do, I will mean it in the nicest possible sense of the term.

I am easily tempted to investigate new problems in operator theory and operator algebras.

A selection of recent papers

    Marcoux, L.W. and Płaneta, A., Quasidiagonal weighted shifts on directed trees (2023) 38pp. to appear in Studia Math.

    Marcoux, L.W., Radjavi, H. and Zhang, Y.H., Around the closure of the set of commutators of idempotents in B(H): biquasitriangularity and factorisation, J. Funct. Anal. 284 (2023) no.8, Paper no. 109854, 45pp.

    Marcoux, L.W., Radjavi, H. and Zhang, Y.H., Around the closures of the set of commutators and the set of differences of idempotent elements in B(H), (2023) 30ms. to appear in the J. Oper. Th.

    Marcoux, L.W., Radjavi, H. and Rosenthal, P., Triangular operator algebras and simultaneous triangularisation, Proc. Amer. Math. Soc. 151 (2023), 755-762.

    Marcoux, L.W., Five Hilbert space problems in operator algebras Complex. Anal. Oper. Theory 16 (2022), no. 8, Paper no. 116, 15pp.

    Marcoux, L.W., Radjavi, H. and Zhang, Y.H., Dispersing representations of semi-simple subalgebras of complex matrices, Linear Algebra Appl. 642 (2022), 160-220.

    Bernik, J., Livshits, L., MacDonald, G., Marcoux, L.W., Mastnak, M. and Radjavi, H., Algebraic degree in spatial matricial numerical ranges of linear operators, Proc. Amer. Math. Soc. 149 (2021), 4083-4097.

    Cramer, Z., Marcoux, L.W. and Radjavi, H., Matrix algebras with a certain compression property, Linear Algebra Appl. 621 (2021), 50-85.

    MacDonald, G., Marcoux, L.W., Mastnak, M., Omladic, M. and Radjavi, H., A note on the structure of matrix *-subalgebras with scalar diagonals, Oper. Matrices 15 (2021), 39-45.

    Marcoux, L.W. and Zhang, Y.H., On Specht's Theorem in UHF C*-algebras, J. Funct. Anal. 280 (2021), no.1, Paper no. 108778, 28pp.

    Marcoux, L.W., Radjavi, H. and Zhang, Y.H., Normal operators with highly incompatible off-diagonal corners, Studia Math. 256 (2021), 73-91.

    Marcoux, L.W., Radjavi, H. and Zhang, Y.H., Off-diagonal corners of subalgebras of L(C^n), Linear Alg. Appl. 607 (2020), 58-88.

    Marcoux, L.W. and Zhang, Y.H., Operators which are polynomially isometric to a normal operators, Proc. Amer. Math. Soc. 148 (2020), 2019-2033.

    Marcoux, L.W. and Sourour, A.R., On the spectrum of the Sylvester-Rosenblum operator acting on triangular algebras, to appear in Operators and Matrices, (2020).

    Marcoux, L.W., On norm-limits of algebraic quasidiagonal operators, J. Operator Th. 83 (2020), 475-494.

    Aghamollaei, G., Marcoux, L.W., and Radjavi, H., Linear preservers of polynomial numerical convex hulls, Lin. Alg. Appl. 575 (2019), 27-34.

    Marcoux, L.W., Radjavi, H., and Yahaghi, B.R., On *-similarity in C*-algebras,Studia Math. 252 (2020), 93-103.

    Clouâtre, R. and Marcoux, L.W., Compact ideals and rigidity of representations for amenable operator algebras, Studia Math. 244 (2019), 25-41.

    Clouâtre, R. and Marcoux, L.W., Residual finite-dimensionality and representations of amenable operator algebras, J. Math. Anal. Appl. 472, (2019), 1346-1368.

    Livshits, L., MacDonald, G., Marcoux, L.W. and Radjavi, H., Hilbert space operators with compatible off-diagonal corners, J. Funct. Anal. 275 (2018), 892-925.

    Marcoux, L.W., Radjavi, H. and Yahaghi, B.R., Reducibility of operator semigroups and values of vector states, Semigroup Forum 95, (2017), 126-158.

    Marcoux, L.W., Omladic, M, Popov., A.I., Radjavi, H. and Yahaghi, B.R., Ranges of vector states on irreducible operator semigroups, Semigroup Forum 95 (2016), 264-304.

    Livshits, L., MacDonald, G., Marcoux, L.W. and Radjavi, H., Universal bounds for positive matrix semigroups, Studia Math. 232 (2016), 143-153.

    Marcoux, L.W. and Popov, A., Abelian, amenable operator algebras are similar to C*-algebras, Duke Math. J. 165 (2016), 2391-2406.

    Bernik, J., Marcoux, L.W., Popov, A.I., and Radjavi, H., On selfadjoint extensions of semigroups of partial isometries, Trans. Amer. Math. Soc. 2016 (2016), 264-304.


    Marcoux, L.W., Radjavi, H., Troscheit, S. and Zhang, Y.H., Stability relations for Hilbert space operators and a problem of Kaplansky, (2023), 45ms.

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I have produced typed course notes for a number of courses taught at the University of Waterloo. They are varying states of readiness, but at least they are available for free. Simply click on the links below.

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Absolutely nothing is more fulfilling than supervision. But, given how poorly remunerated doing absolutely nothing is, I have chosen to offer what humble services I can in this capacity.

All kidding aside (ok, write down this date as you will not hear me say that again), I have had the extremely good fortune to have supervised some wonderful students, at the undergraduate, Masters and Ph.D. levels.

Ph.D. students

  • Cramer, Z. (2019) Compressible matrix algebras and the distance from projections to nilpotents , University of Waterloo.
  • Chan, K.C. (2012) Digraph algebras over discrete pre-ordered groups, University of Waterloo.
  • Dostál, M. (1998) Closures of (U+K)-orbits of essentially normal models, University of Alberta.

Masters students

  • Sarkowicz, P. (2019) Exact C*-algebras and the Kirchberg-Phillips nuclear embedding theorem. University of Waterloo.
  • Eifler, K. (2016) (co-supervised with M. Kennedy) Graph C*-algebras, an introduction. , University of Waterloo.
  • Cramer, Z. (2015) Normal limits of nilpotent and normal operators similarity orbits in purely infinite C*-algebras , University of Waterloo.
  • Haley, J. (2015) Strongly reductive operators and strongly reductive operator algebras , University of Waterloo.
  • Harris, S. (2015) Kadison similarity problem and similarity degree , University of Waterloo.
  • Yu, P. (2015) Spans of projections in certain C*-algebras , University of Waterloo.
  • Chow, S.S. (2012) Graph algebras of real rank zero, University of Waterloo.
  • Onuma, K. (2011) Linear mappings between Banach algebras that preserve spectral properties, University of Waterloo.
  • Boey, E. (2010) On the modular theory of von Neumann algebras, University of Waterloo.
  • Al-Ahmari, A. (2006) Almost commuting matrices versus nearly commuting matrices, University of Waterloo.
  • Georgescu, M. (2006) (co-supervised with B.E. Forrest), On the similarity of operator algebras to C*-algebras, University of Waterloo.
  • Pollock, D. (2004) (co-supervised with K.R. Davidson) On C*-envelopes of a special class of limit algebras, University of Waterloo.
  • Gusba, S. (1999) Connectedness of the invertible group of a nest algebra, University of Alberta.

Undergraduate students

  • Patrón-Fonseca, O. (2023) Quasitriangularity in Hilbert space, University of Waterloo.
  • Jelinsky, A. (2022) Introduction to operator algebras, University of Waterloo.
  • Xu, T. (2022) Introduction to operator algebras, University of Waterloo.
  • Ala, M. (2021) Amenability of operator algebras, University of Waterloo.
  • Shiner, A. (2019) Similarity, amenability and the total reduction property, University of Waterloo.
  • Suan, C. (2019) The almost-invariant subspace problem, University of Waterloo.
  • Sarkowicz, P. (2018) Nuclear C*-algebras and Kadison's similarity problem, University of Waterloo.
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Contact Us

Mailing Address

Department of Pure Mathematics
University of Waterloo
Waterloo, Ontario
Canada, N2L 3G1

Phone: 519-888-4567
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