A REMARK ON THE GEOMETRY OF SPACES OF FUNCTIONS WITH PRIME FREQUENCIES

摘要

For any positive integer r, denote by P_r the set of all integers γ ∈ Z having at most r prime divisors. We show that CP_r (T), the space of all continuous functions on the circle T whose Fourier spectrum lies in P_r, contains a complemented copy of ?~1. In particular, CP_r (T) is not isomorphic to C(T), nor to the disc algebra A(D). A similar result holds in the L~1 setting.