Bernstein and Kantorovich polynomials diminish the Λ-variation

We prove the Λ-variation diminishing property of the Bernstein and Kantorovich polynomials. Next we apply this result to characterize the space CΛBVc as the closure of the space of polynomials in the ‖⋅‖Λ norm. A new proof of the separability of CΛBVc is given.