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

Citation
As. Granero et H. Hudzik, THE CLASSICAL BANACH-SPACES L(PHI) H(PHI), Proceedings of the American Mathematical Society, 124(12), 1996, pp. 3777-3787
Citations number
15
Categorie Soggetti
Mathematics, General",Mathematics,Mathematics
ISSN journal
00029939
Volume
124
Issue
12
Year of publication
1996
Pages
3777 - 3787
Database
ISI
SICI code
0002-9939(1996)124:12<3777:TCBLH>2.0.ZU;2-1
Abstract
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 .