Jireh Loreaux

Jireh Loreaux

Assistant Professor of Mathematics

Southern Illinois University Edwardsville

Interests

  • Operator theory
  • Operator algebras
  • Matrix theory

Education

  • PhD in Mathematics, 2016

    University of Cincinnati

  • BA with honors in Mathematics, 2010

    University of Cincinnati

Publications

Search or sort by year by filtering publications.
Jireh Loreaux, Ping Wong Ng, Arindam Sutradhar (2021). $K_1$-injectivity of the Paschke dual algebra, and uniqueness. preprint.

essential codimension arXiv: 2106.13370 [math.OA]

Jireh Loreaux, Sasmita Patnaik (2021). Closedness of the orbit-closed $C$-numerical range and submajorization. preprint.

numerical range arXiv: 2106.11205 [math.FA]

Jireh Loreaux, Gary Weiss (2021). Matrix splitting and ideals in $B(H)$. Operators and Matrices (to appear).

arXiv: 2103.09215 [math.FA]

Jireh Loreaux, Sasmita Patnaik (2021). Convexity of the orbit-closed $C$-numerical range and majorization. Linear and Multilinear Algebra, (to appear).

numerical range doi: 10.1080/03081087.2021.1895702 arXiv: 2009.01300 [math.FA]

Jireh Loreaux, Gary Weiss (2020). On diagonals of operators: selfadjoint, normal and other classes. Operator Theory: Themes and Variations — Conference Proceedings, Timişoara, July 2–6, 2018, pp. 193–214.

diagonals of operators arXiv: 1905.09987 [math.FA]

Jireh Loreaux, Ping Wong Ng (2020). Remarks on essential codimension. Integral Equations and Operator Theory, vol. 92 (1), pp. 1–35.

essential codimension doi: 10.1007/s00020-019-2560-0 arXiv: 1902.09367 [math.OA]

Jireh Loreaux (2019). Restricted diagonalization of finite spectrum normal operators and a theorem of Arveson. Journal of Operator Theory, vol. 81 (2), pp. 257–272..

essential codimension diagonals of operators doi: 10.7900/jot.2017dec01.2221 arXiv: 1712.06554 [math.OA] html

Jireh Loreaux, Gary Weiss (2018). Traces on ideals and the commutator property. Operator Theory: Themes and Variations — Conference Proceedings, Timişoara, June 27–July 2, 2016, pp. 147–155.

arXiv: 1712.06702 [math.FA]

John Jasper, Jireh Loreaux, Gary Weiss (2018). Thompson's theorem for compact operators and diagonals of unitary operators. Indiana University Mathematics Journal, vol. 67 (1), pp. 1–27.

diagonals of operators doi: 10.1512/iumj.2018.67.6291 arXiv: 1602.08435 [math.FA]

Victor Kaftal, Jireh Loreaux (2017). Kadison's Pythagorean Theorem and essential codimension. Integral Equations and Operator Theory, vol. 87 (4), pp. 565–580.

essential codimension diagonals of operators doi: 10.1007/s00020-017-2365-y arXiv: 1609.06754 [math.OA] html

Jireh Loreaux, Gary Weiss (2016). Diagonality and idempotents with applications to problems in operator theory and frame theory. Journal of Operator Theory, vol. 75 (1), pp. 91–118.

diagonals of operators doi: 10.7900/jot.2014nov05.2054 arXiv: 1410.7441 [math.FA]

Jireh Loreaux, Gary Weiss (2015). Majorization and a Schur–Horn Theorem for positive compact operators, the nonzero kernel case. Journal of Functional Analysis, vol. 268 (3), pp. 703–731.

diagonals of operators doi: 10.1016/j.jfa.2014.10.020 arXiv: 1403.4917 [math.FA]

Recent Posts

Resources

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Projects

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All Diagonals Essential Codimension

Diagonals of operators

a project to characterize diagonals of operators, especially selfadjoint operators, in terms of spectral data.

Essential codimension

a project to generalize the notion of essential codimension due to Brown–Douglas–Fillmore, as well as to understand its ramifications.

Numerical range

This project investigates generalizations of the standard numerical range and their associated properties.

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