On the diagonal of Riesz operators on Banach lattices

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

This paper extends the well-known Ringrose theory for compact operators to polynomially Riesz operators on Banach spaces. The particular case of an ideal-triangularizable Riesz operator on an order continuous Banach lattice yields that the spectrum of such operator lies on its diagonal, which motivates the systematic study of an abstract diagonal of a regular operator on an order complete vector lattice $E$. We prove that the class $\mathscr D$ of regular operators for which the diagonal coincides with the atomic diagonal is always a band in $\mathcal L_r(E)$, which contains the band of abstract integral operators. If $E$ is also a Banach lattice, then $\mathscr D$ contains positive Riesz and positive AM-compact operators.

• Jezik: Angleški jezik
• Ključne besede: vector lattices, Banach lattices, Riesz operators, diagonal of an operator
• 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: 2024
• Št. strani: Str. S137-S151
• Številčenje: Vol. 47, iss. S1
• PID: 20.500.12556/RUL-155239
• UDK: 517.9
• ISSN pri članku: 1607-3606
• DOI: 10.2989/16073606.2023.2287829
• COBISS.SI-ID: 188345347
• Datum objave v RUL: 21.03.2024

Gradivo je del revije

• Naslov: Quaestiones mathematicae
• Skrajšan naslov: Quaest. math.
• Založnik: Taylor & Francis, National Inquiry Services Centre, South African Mathematical Society
• ISSN: 1607-3606
• COBISS.SI-ID: 514029849

Projekti

• Financer: ARIS - Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
• Številka projekta: P1-0222
• Naslov: Algebra, teorija operatorjev in finančna matematika

• Financer: ARIS - Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
• Številka projekta: N1-0217
• Naslov: Nekomutativna realna algebraična geometrija s sledjo