20.500.12556/DiRROS-28921 On positive automorphisms of algebras of operators on atomic Archimedean vector lattices 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. vector lattices order algebra automorphisms inner automorphisms atom order continuous operators true false true Angleški jezik Slovenski jezik Neznano 2026-04-14 10:29:43 2026-04-14 10:29:44 2026-04-15 03:57:35 0000-00-00 00:00:00 2026 0 0 26 str. iss. 2, article no. 30 Vol. 30 Apr. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-04-01 517.9 1385-1292 10.1007/s11117-026-01190-y 275059203 s11117-026-01190-y.pdf s11117-026-01190-y.pdf 1 A3FB5F28894392B637D4DAAA6142F411 f708a1b9d9501de0f99df916d9a6d61ba4108792440fd4cf485d36f19ca8246a 16a96359-37dd-11f1-9cc3-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=43139 https://link.springer.com/article/10.1007/s11117-026-01190-y 1 18ae0dc1-37dc-11f1-9cc3-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=43136 Inštitut za matematiko, fiziko in mehaniko 0 0 0