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Pointwise products of some Banach function spaces and factorization
Institute of Mathematics of Electric Faculty, Poznań University of Technology.
Institute of Mathematics of Electric Faculty, Poznań University of Technology.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0002-9584-4083
2014 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 266, no 2, p. 616-659Article in journal (Refereed) Published
Abstract [en]

The well-known factorization theorem of Lozanovskiĭ may be written in the form L1≡E⊙E′, where ⊙ means the pointwise product of Banach ideal spaces. A natural generalization of this problem would be the question when one can factorize F through E, i.e., when F≡E⊙M(E,F), where M(E,F) is the space of pointwise multipliers from E to F. Properties of M(E,F) were investigated in our earlier paper [41] and here we collect and prove some properties of the construction E⊙F. The formulas for pointwise product of Calderón–Lozanovskiĭ Eφ-spaces, Lorentz spaces and Marcinkiewicz spaces are proved. These results are then used to prove factorization theorems for such spaces. Finally, it is proved in Theorem 11 that under some natural assumptions, a rearrangement invariant Banach function space may be factorized through a Marcinkiewicz space.

Place, publisher, year, edition, pages
2014. Vol. 266, no 2, p. 616-659
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-13256DOI: 10.1016/j.jfa.2013.10.028Local ID: c724094a-be49-42f7-89f4-7aa1fdc8fd30OAI: oai:DiVA.org:ltu-13256DiVA, id: diva2:986208
Note
Validerad; 2014; 20131120 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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