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Inclusion mappings between Orlicz sequence spaces
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0002-9584-4083
Adam Mickiewicz University, Poznan.
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
Abstract [en]

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.
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-13430DOI: 10.1006/jfan.2000.3624Local ID: ca73b250-b04a-11db-840a-000ea68e967bOAI: oai:DiVA.org:ltu-13430DiVA: diva2:986383
Note
Validerad; 2000; 20070110 (kani)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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