On the denseness of span{xλj (1 −x)1−λj } in C0([0, 1])

Associated with a sequence Λ = (λj )∞j =0 of distinct exponents λj ∈ [0, 1], we define H(Λ) := span xλ0 (1−x)1−λ0, xλ1 (1−x)1−λ1 , . . . ⊂ C [0, 1] . Answering a question of Giuseppe Mastroianni, we show that H(Λ) is dense in C0[0, 1] := f ∈ C[0, 1]: f (0) = f (1) = 0 in the uniform norm on [0, 1] if and only if ∞ j=0 1/2 − |1/2 −λj | =∞. © 2006 Elsevier Inc. All rights reserved