كليدواژه :
Vector-valued Lipschitz space , Continuously differentiable vector-valued function , Vectorvalued measure , Approximation
چكيده لاتين :
Let (X, d) be a compact metric space, S* a complex Banach space and S its dual, and α ∈ (0, 1).
Using S* -valued measure theory and duality, we give a criterion for the density of a subspace of lipα(X, S).
In the case where X = [a, b], we conclude that Lip1(X, S) is dense in lipα(X, S). Also using Bochner spaces and duality we show that C1([a, b], S), the space of continuously differentiable S-valued functions on [a, b],is dense in lipα([a, b], S).
