Positive self-commutators of positive operators

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

We consider a positive operator $A$ on a Hilbert lattice such that its self-commutator $C = A^* A - A A^*$ is positive. If $A$ is also idempotent, then it is an orthogonal projection, and so $C = 0$. Similarly, if $A$ is power compact, then $C = 0$ as well. We prove that every positive compact central operator on a separable infinite-dimensional Hilbert lattice ${\mathcal H}$ is a self-commutator of a positive operator. We also show that every positive central operator on ${\mathcal H}$ is a sum of two positive self-commutators of positive operators.

• Language: English
• Keywords: Banach lattices, positive operators, 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
• Year: 2025
• Number of pages: 17 str.
• Numbering: Vol. 29, iss. 3, art. 43
• PID: 20.500.12556/RUL-175179
• UDC: 517.9
• ISSN on article: 1385-1292
• DOI: 10.1007/s11117-025-01135-x
• COBISS.SI-ID: 240577795
• Publication date in RUL: 20.10.2025

Record is a part of a journal

• Title: Positivity
• Shortened title: Positivity
• Publisher: Springer Nature
• ISSN: 1385-1292
• COBISS.SI-ID: 512122649

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• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
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