Representation of Banach ideal spaces and factorization of operators
2005 (English)In: Canadian Journal of Mathematics - Journal Canadien de Mathematiques, ISSN 0008-414X, E-ISSN 1496-2479, Vol. 57, no 5, 897-940 p.Article in journal (Refereed) Published
Representation theorems are proved for Banach ideal spaces with the Fatou property which are built by the Calderón-Lozanovskiǐ construction. Factorization theorems for operators in spaces more general than the Lebesgue Lp spaces are investigated. It is natural to extend the Gagliardo theorem on the Schur test and the Rubio de Francia theorem on factorization of the Muckenhoupt Ap weights to reflexive Orlicz spaces. However, it turns out that for the scales far from Lp-spaces this is impossible. For the concrete integral operators it is shown that factorization theorems and the Schur test in some reflexive Orlicz spaces are not valid. Representation theorems for the Calderón-Lozanovskiǐ construction are involved in the proofs
Place, publisher, year, edition, pages
2005. Vol. 57, no 5, 897-940 p.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:ltu:diva-3466Local ID: 14c6afd0-a54a-11db-8975-000ea68e967bOAI: oai:DiVA.org:ltu-3466DiVA: diva2:976324
Validerad; 2005; 20070116 (evan)2016-09-292016-09-29Bibliographically approved