Positive self-commutators of positive operators

Drnovšek, Roman (avtor), Kandić, Marko (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: Banach lattices, positive operators, commutators
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2025
• Št. strani: 17 str.
• Številčenje: Vol. 29, iss. 3, art. 43
• PID: 20.500.12556/RUL-175179
• UDK: 517.9
• ISSN pri članku: 1385-1292
• DOI: 10.1007/s11117-025-01135-x
• COBISS.SI-ID: 240577795
• Datum objave v RUL: 20.10.2025

Gradivo je del revije

• Naslov: Positivity
• Skrajšan naslov: Positivity
• Založnik: Springer Nature
• ISSN: 1385-1292
• COBISS.SI-ID: 512122649

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.