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Copyright © 2021 L.W. Marcoux, Esq.
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Welcome to my homepage

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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 and nserc usras.

    I serve on a bunch of committees.

Teaching testimonials

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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Research

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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 permanence properties of compressions of operator algebras.

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

A selection of recent papers

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

    Marcoux, L.W., Radjavi, H. and Zhang, Y.H., Normal operators with highly incompatible off-diagonal corners, Studia Math. 256 (2021), 73-92.

    Marcoux, L.W. and Zhang, Y.H., On Specht's Theorem in UHF C*-algebras, J. Funct. Anal. 280 (2021).

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

    Marcoux, L.W. and Sourour, A.R., On the spectrum of the Sylvester-Rosenblum operator acting on triangular algebras, Oper. Matrices 14 (2020), 401-416.

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

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

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

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

    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.

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

Preprints

    Bernik, J., Livshits, L., MacDonald, G., Marcoux, L.W., Mastnak, M. and Radjavi, H., Algebraic degree in spatial matricial numerical ranges of linear operators, (2020).

    Cramer, Z., Marcoux, L.W. and Radjavi, H., Matrix algebras with a certain compression property, (2019).

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Teaching

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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Supervision

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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

  • 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

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Mailing Address

L.W. Marcoux
Department of Pure Mathematics
University of Waterloo
Waterloo, Ontario
Canada, N2L 3G1

Phone: 519-888-4567
Email: Laurent.Marcoux AT uwaterloo DOT ca
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