On linearization and uniqueness of preduals

We study strong linearizations and the uniqueness of preduals of locally convex Hausdorff spaces of scalar-valued functions. Strong linearizations are special preduals. A locally convex Hausdorff space (Formula presented.) of scalar-valued functions on a nonempty set (Formula presented.) is said to admit a strong linearization if there are a locally convex Hausdorff space (Formula presented.), a map (Formula presented.), and a topological isomorphism (Formula presented.) such that (Formula presented.) for all (Formula presented.). We give sufficient conditions that allow us to lift strong linearizations from the scalar-valued to the vector-valued case, covering many previous results on linearizations, and use them to characterize the bornological spaces (Formula presented.) with (strongly) unique predual in certain classes of locally convex Hausdorff spaces.