Bernstein and Kantorovich polynomials diminish the $\Lambda$-variation

Abstract

We prove the $\Lambda$-variation diminishing property of the Bernstein and Kantorovich polynomials. Next we apply this result to characterize the space $C\Lambda B{V}_c$ as the closure of the space of polynomials in the $\Lambda BV$ norm. A new proof of the separability of $C\Lambda B{V}_c$ is given.

15 pages; corrected typos, reformulated argument before Observation 1, reformulated Theorem 7, results unchanged