Douglas Farenick

Contact Info

Research Interests

Operator theory

Current Courses

PMTH 092 Intermediate Algebra II

Biography

I received my Ph.D. from the University of Toronto, working under the supervision of Chandler Davis. My contributions to knowledge include two books, 50+ refereed journal publications, and numerous lectures in Canada and abroad. I am known mainly for research works in noncommutative convexity, Toeplitz operators and matrices, local multiplier algebras, operator systems and algebras, and quantum probability measures.

I teach courses ranging from 1^st-year undergraduate courses through to courses for doctoral students: calculus (single variable, several variable, vector, applied), linear algebra, mathématiques discrètes, differential equations, modern algebra, complex analysis, Lie groups, measure theory and integration, functional analysis, operator algebras, quantum information theory, topology, history of mathematics. I also developed online courses in pre-college algebra, pre-calculus and modelling, and applied calculus. A rewarding highlight of my teaching career was the one month I spent in 2017 teaching at the African Institute for the Mathematical Sciences, Kigali, Rwanda. I am fortunate to have taught or worked closely with many young people over the years, supporting their growth as people and scholars or professionals; some even became mathematics professors and researchers! 

I am also been lucky to be surrounded by colleagues and friends who give generously of their time and expertise to initiatives such as the Science Camps for Saskatchewan Indigenous Youth and the Turtle Island Indigenous Science Conference.

Recent Publications

1) Farenick, Douglas; McBurney, Michelle.  Toeplitz separability, entanglement, and complete positivity using operator system duality.  Proc. Amer. Math. Soc. Ser. B 10 (2023), 114–128.

2) Farenick, Douglas; Tessier, Ryan Purity of the embeddings of operator systems into their C^∗- and injective envelopes. Pacific J. Math. 317 (2022), no. 2, 317–338.

3) Farenick, Douglas; Huntinghawk, Farrah; Masanika, Adili; Plosker, Sarah Corrigendum to "Complete order equivalence of spin unitaries'' [Linear Algebra Appl. 610 (2021) 1–28]. Linear Algebra Appl. 635 (2022), 201–202.

4) Farenick, Douglas; Ojo, Oluwatobi Ruth; Plosker, Sarah. Universality of Weyl unitaries. Linear Algebra Appl. 634 (2022), 57–76.

Books

1) D. Farenick, Fundamentals of Functional Analysis. Springer, New York. 2016.

2) D. Farenick, Algebras of Linear Transformations. Springer, New York. 2001.