Positive commutators of positive square-zero operators

Drnovšek, Roman (author), Kandić, Marko (author)

In this paper we first consider the question which nonnegative matrices are commutators of nonnegative square-zero matrices. Then, we treat infinite-dimensional analogues of these results for operators on the Banach lattices $L^p[0,1]$ and $\ell^p(1\le p<\infty)$. In the last setting we need to extend the notion of the nonnegative rank of a nonnegative matrix.

• Language: English
• Keywords: Banach lattices, positive operators, nonnegative matrices, commutators
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.07.2026
• Year: 2026
• Number of pages: Str. 56-67
• Numbering: Vol. 740
• PID: 20.500.12556/RUL-181754
• UDC: 517.9
• ISSN on article: 0024-3795
• DOI: 10.1016/j.laa.2026.03.015
• COBISS.SI-ID: 275200771
• Publication date in RUL: 15.04.2026

Record is a part of a journal

• Title: Linear algebra and its applications
• Shortened title: Linear algebra appl.
• Publisher: Elsevier
• ISSN: 0024-3795
• COBISS.SI-ID: 1119247

Licences

• License: CC BY-NC 4.0, Creative Commons Attribution-NonCommercial 4.0 International
• Link: http://creativecommons.org/licenses/by-nc/4.0/
• Description: A creative commons license that bans commercial use, but the users don’t have to license their derivative works on the same terms.

Secondary language

• Language: Slovenian
• Keywords: Banachove mreže, pozitivni operatorji, nenegativne matrike, komutatorji

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P1-0222
• Name: Algebra, teorija operatorjev in finančna matematika

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: J1-50002
• Name: Realna algebraična geometrija v matričnih spremenljivkah