Inclusion mappings between Orlicz sequence spaces
2000 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 176, no 2, 264-279 p.Article in journal (Refereed) Published
It is shown that if ℓis an Orlicz sequence space, then the space ℓw1(ℓ) of weakly summable sequences in ℓis continuously embedded into ℓ(ℓ2) (resp., into ℓ(ℓ)) whenever t ( ) is equivalent to a concave function (resp., a convex function and is a supermultiplicative function). By combining the above results with the interpolation theory we proved continuous inclusions between spaces ℓw1(ℓ0) and ℓφ(ℓ1), where ℓ0 ℓ1 and φ is a certain Orlicz function depending on 0 and 1. In particular, if 0 and 1 are power functions we obtain the well known result on (r, 1)-summability of the inclusion mappings between ℓp-spaces proved independently by G. Bennett (1973, J. Funct. Anal.13, 20-27) and B. Carl (1974, Math. Nachr.63, 253-360).
Place, publisher, year, edition, pages
2000. Vol. 176, no 2, 264-279 p.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:ltu:diva-13430DOI: 10.1006/jfan.2000.3624Local ID: ca73b250-b04a-11db-840a-000ea68e967bOAI: oai:DiVA.org:ltu-13430DiVA: diva2:986383
Validerad; 2000; 20070110 (kani)2016-09-292016-09-29Bibliographically approved