THE CLASSICAL BANACH-SPACES L(PHI) H(PHI)

In this paper we study some structural and geometric properties of the quotient Banach spaces l(phi)(I)/h(phi)(S), where I is an arbitrary s et, phi is an Orlicz function, l(phi)(I) is the corresponding Orlicz s pace on I and h(phi)(S) = {x epsilon l(phi)(I) : For All lambda > 0, T here Exists s is an element of S such that I phi(x-s/lambda) < infinit y}, S being the ideal of elements with finite support. The results we obtain here extend and complete the ones obtained by Leonard and Whitf ield (Rocky Mountain J. Math. 13 (1983), 531-539). We show that l(phi) /(I)/h(phi)(S) is nota dual space, that Ext(B-l phi(I/h phi(S))) = 0, if phi(t) > 0 for every t > 0, that S-l phi(I/h phi(S)) has no smooth points, that it cannot be renormed equivalently with a strictly convex or smooth norm, that l(phi)(I)/h(phi)(S) is a Grothendieck space; etc .