Kruse, KarstenKarstenKruse2024-08-012024-08-012024-06-01Rendiconti del Circolo Matematico di Palermo 73 (4): 1591-1615 (2024)https://hdl.handle.net/11420/48603We study the problem of existence of preduals of locally convex Hausdorff spaces. We derive necessary and sufficient conditions for the existence of a predual with certain properties of a bornological locally convex Hausdorff space X. Then we turn to the case that X=F(Ω) is a space of scalar-valued functions on a non-empty set Ω and characterise those among them which admit a special predual, namely a strong linearisation, i.e. there are a locally convex Hausdorff space Y, a map δ:Ω→Y and a topological isomorphism T:F(Ω)→Yb′ such that T(f)∘δ=f for all f∈F(Ω).en1973-44092024415911615Springer Italiahttps://creativecommons.org/licenses/by/4.0/Dual spaceLinearisationMixed topologyPredualNatural Sciences and Mathematics::510: MathematicsJournal Article10.15480/882.1318910.1007/s12215-024-01004-810.15480/882.13189Journal Article