## Jireh Loreaux

### 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.
(2021). Matrix splitting and ideals in $B(H)$. Operators and Matrices (to appear).

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

(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.

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

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

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

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

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

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

(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.

# Recent Posts

### Resources

General software KeePassX — a (FOSS) password manager (based on KeePass by Bruce Schneier) GNU OS — a free/libre and open source (FOSS) operating system (less the kernel) Arch Linux — a GNU/Linux distribution with rolling releases and a Keep It Simple philosophy Emacs — the king of text editors Vim — a lesser, but still useful, text editor Git — a distributed version control system Magit — a Git Porcelain inside Emacs nXML — a new XML mode for Emacs LibreOffice — a (FOSS) office suite (for when someone sends you an evil .

### How to install $\LaTeX$

So, you want to produce professional quality typesetting of mathematical formulae? Look no further. You will need a distribution of LaTeX. A tremendous resource in addition to (or perhaps even in place of) this article is the LaTeX Project.

# Projects

#### 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.