20.500.12556/DiRROS-29841 Similarities of subspace lattices in Banach spaces A collineation of a subspace lattice ${\mathfrak L}$ in a complex Banach space ${\mathscr X}$ is an invertible operator $S$ on ${\mathscr X}$ with the property that the image $S{\mathscr M}$ of a subspace ${\mathscr M}$ belongs to ${\mathfrak L}$ if and and only if ${\mathscr M}$ belongs to it. Hence, $S$ is a collineation of ${\mathfrak L}$ if and only if it implements an order automorphism of ${\mathfrak L}$. We study the group ${\rm Col}({\mathfrak L})$ of all collineations of ${\mathfrak L}$ and its subgroup ${\rm Grp}({\rm Alg}({\mathfrak L}))$ of all invertible operators that fix every subspace in ${\mathfrak L}$. We show that ${\rm Grp}({\rm Alg}({\mathfrak L}))$ is a normal subgroup of ${\rm Col}({\mathfrak L})$; moreover, if ${\mathfrak L}$ is a reflexive subspace lattice, then ${\rm Col}({\mathfrak L})$ is the normalizer of ${\rm Grp}({\rm Alg}({\mathfrak L}))$ in the group of all invertible operators on ${\mathscr X}$. One of the main questions that we consider is whether ${\rm Grp}({\rm Alg}({\mathfrak L}))$ is a complemented subgroup in ${\rm Col}({\mathfrak L})$. For certain subspace lattices ${\mathfrak L}$, such as some realizations of the diamond or the double triangle, some nests in the space of continuous functions on $[0,1]$, and the classical Volterra nest in $L^1[0,1]$, we characterize the complement of ${\rm Grp}({\rm Alg}({\mathfrak L}))$ in ${\rm Col}({\mathfrak L})$. On the other hand, for the Volterra nests in $L^p[0,1]$, where $1<p<\infty$, a further study is needed, and we prove only some partial results. subspace lattice collineation normalizer reflexive lattice Volterra nest Banachovi prostori mreže true false true Angleški jezik Slovenski jezik Neznano 2026-06-08 12:08:05 2026-06-08 12:08:06 2026-06-09 03:49:21 0000-00-00 00:00:00 2026 0 0 20 str. iss. 1, article no. 130857 Vol. 564 Dec. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-12-01 517.9 0022-247X 10.1016/j.jmaa.2026.130857 280774403 1-s2.0-S0022247X26004695-main.pdf 1-s2.0-S0022247X26004695-main.pdf 1 EC27BD0D5B28A00385983D587C624D27 f6aecc4b40267e75c52c424909204b5e3179b49938843baa9ef8528857d70008 80bc9fc4-6322-11f1-9215-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=44889 https://www.sciencedirect.com/science/article/pii/S0022247X26004695 1 f2d468a8-6321-11f1-9215-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=44885 Inštitut za matematiko, fiziko in mehaniko 0 0 0