ON SOME PROBLEMS IN THE SPACE C(n)[0,1]

We consider the so called alpha - Duhamel product, denoted [GRAPHICS] , on the space a C-(n)[0,1] and prove that, with this product, this space has the structure of a unital Banach algebra, and then show that its maximal ideal space consists of the homomorphism phi(alpha) defined by phi(alpha)(integral)= integral (alpha). Moreover, we consider the usual convolution product [GRAPHICS] and study the [GRAPHICS] -generators of the Banach algebra (C-(n)[0,1], [GRAPHICS] ). Some other related questions are also discussed. Our results improve the work of [2,3,4,5] where the case alpha = 0 was considered.