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

Associated with a sequence Λ=(λj)j=0∞ of distinct exponents λj∈[0,1]λj∈[0,1], we defineH(Λ):=span{xλ0(1−x)1−λ0,xλ1(1−x)1−λ1,…}⊂C([0,1]).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)H(Λ) is dense inC0[0,1]:={f∈C[0,1]:f(0)=f(1)=0} in the uniform norm on [0,1][0,1] if and only if∑j=0∞(1/2−|1/2−λj|)=∞.