| Title: | On the diagonal of Riesz operators on Banach lattices |
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| Authors: | ID Drnovšek, Roman (Author)
ID Kandić, Marko (Author) |
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| Files: |  PDF - Presentation file, download (589,79 KB)
MD5: 1A99C08F98B1932D5070979D4E06B2EC
 URL - Source URL, visit https://www.tandfonline.com/doi/abs/10.2989/16073606.2023.2287829
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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. |
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| Keywords: | vector lattices, Banach lattices, Riesz operators, diagonal of an operator |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | str. S137-S151 |
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| Numbering: | Vol. 47, iss. sup1 |
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| PID: | 20.500.12556/DiRROS-21315  |
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| UDC: | 517.9 |
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| ISSN on article: | 1607-3606 |
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| DOI: | 10.2989/16073606.2023.2287829 |
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| COBISS.SI-ID: | 188345347 |
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| Publication date in DiRROS: | 24.01.2025 |
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| Views: | 595 |
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| Downloads: | 338 |
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