ON A CLASS OF BANACH FUNCTION SPACES AND ITS RELATION TO SOME CLASSICAL SPACES

Assume that F denotes a specific space in the class Fα,p constructed by H. Khodabakhshiani as a class of separable Banach function spaces similar to the well-known James function spaces. In this note, we prove that lp(α) is isomorphic to a complemented subspace of Fα,p, and that Fα,2 is a closed subspace of the Waterman-Shiba space αBV ².