| Title: | On positive automorphisms of algebras of operators on atomic Archimedean vector lattices |
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| Authors: | ID Cigler, Gregor (Author)
ID Kandić, Marko (Author) |
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| Files: |  PDF - Presentation file, download (377,43 KB)
MD5: A3FB5F28894392B637D4DAAA6142F411
 URL - Source URL, visit https://link.springer.com/article/10.1007/s11117-026-01190-y
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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: | Let $X$ be an Archimedean vector lattice. We investigate subalgebras of ${\mathscr L}(X)$ consisting of regular operators that contain all rank-one operators of the form $a \otimes \varphi_b$, where $a$ and $b$ are atoms of $X$ and $\varphi_b$ denotes the coordinate functional associated with $b$. Our main result shows that every positive automorphism of such a subalgebra contained in ${\mathscr L}(c_{00}(\Lambda))$, is necessarily spatial, meaning that it is implemented by a transformation of the form $T \mapsto P D\, T\, D^{-1} P^{-1}$, where $P$ is a permutation operator and $D$ is a positive diagonal operator. We also use the Kakutani representation theorem to establish that every finite-dimensional vector subspace of $X$ is order closed. |
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| Keywords: | vector lattices, order algebra automorphisms, inner automorphisms, atom, order continuous operators |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.04.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | 26 str. |
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| Numbering: | Vol. 30, iss. 2, article no. 30 |
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| PID: | 20.500.12556/DiRROS-28921  |
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| UDC: | 517.9 |
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| ISSN on article: | 1385-1292 |
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| DOI: | 10.1007/s11117-026-01190-y |
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| COBISS.SI-ID: | 275059203 |
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| Note: |
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| Publication date in DiRROS: | 14.04.2026 |
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| Views: | 126 |
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| Downloads: | 87 |
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