On the diagonal of Riesz operators on Banach lattices

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

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.

• Language: English
• Keywords: vector lattices, Banach lattices, Riesz operators, diagonal of an operator
• 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: 2024
• Number of pages: Str. S137-S151
• Numbering: Vol. 47, iss. S1
• PID: 20.500.12556/RUL-155239
• UDC: 517.9
• ISSN on article: 1607-3606
• DOI: 10.2989/16073606.2023.2287829
• COBISS.SI-ID: 188345347
• Publication date in RUL: 21.03.2024

Record is a part of a journal

• Title: Quaestiones mathematicae
• Shortened title: Quaest. math.
• Publisher: Taylor & Francis, National Inquiry Services Centre, South African Mathematical Society
• ISSN: 1607-3606
• COBISS.SI-ID: 514029849

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: N1-0217
• Name: Nekomutativna realna algebraična geometrija s sledjo