On the nonnegative rank of positive operators

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

In this paper, we introduce the concept of a nonnegative rank of a positive operator $T: X \to Y$ between ordered vector spaces. In the case of nonnegative matrices, our definition agrees with the standard definition of a nonnegative rank. Under some natural and mild assumptions on the cone $Y_+$, we prove that the nonnegative rank and the rank agree whenever the rank is at most two. This can be considered as the infinite-dimensional version of [6, Theorem 4.1]. We also provide an example of a positive rank-three operator on the Banach lattice $C[0, 1]$ with an infinite nonnegative rank.

• Language: English
• Keywords: nonnegative rank, ordered vector spaces, positive operators, Yudin cone
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: Str. 3689-3704
• Numbering: Vol. 299, iss. 11
• PID: 20.500.12556/RUL-190995
• UDC: 517.9
• ISSN on article: 0025-584X
• DOI: 10.1002/mana.70262
• COBISS.SI-ID: 304519683
• Publication date in RUL: 10.11.2026

Record is a part of a journal

• Title: Mathematische Nachrichten
• Shortened title: Math. Nachr.
• Publisher: Wiley
• ISSN: 0025-584X
• COBISS.SI-ID: 25915392

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: nenegativni rang, urejeni vektorski prostori, pozitivni operatorji

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