| Title: | Positive self-commutators of positive operators |
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| Authors: | ID Drnovšek, Roman (Author)
ID Kandić, Marko (Author) |
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| Files: |  PDF - Presentation file, download (280,94 KB)
MD5: 8588752116FD4D80DA269D761CD855FB
 URL - Source URL, visit https://link.springer.com/article/10.1007/s11117-025-01135-x
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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: | 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. |
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| Keywords: | Banach lattices, positive operators, commutators |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.07.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 17 str. |
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| Numbering: | Vol. 29, iss. 3, article no. 43 |
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| PID: | 20.500.12556/DiRROS-23900  |
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| UDC: | 517.9 |
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| ISSN on article: | 1385-1292 |
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| DOI: | 10.1007/s11117-025-01135-x |
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| COBISS.SI-ID: | 240577795 |
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| Publication date in DiRROS: | 20.10.2025 |
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| Views: | 246 |
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| Downloads: | 96 |
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| Metadata: |    |
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