Abstract
We introduce a new class mathcal {FV}(Omega ,E) of weighted spaces of functions on a set Omega with values in a locally convex Hausdorff space E which covers many classical spaces of vector-valued functions like continuous, smooth, holomorphic or harmonic functions. Then we exploit the construction of mathcal {FV}(Omega ,E) to derive sufficient conditions such that mathcal {FV}(Omega ,E) can be linearised, i.e. that mathcal {FV}(Omega ,E) is topologically isomorphic to the varepsilon-product mathcal {FV}(Omega )varepsilon E where mathcal {FV}(Omega ):=mathcal {FV}(Omega ,mathbb {K}) and mathbb {K} is the scalar field of E.
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