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Banach function lattices which are AM-spaces
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2000 (English)In: Scientiae mathematicae Japonicae, ISSN 1346-0862, E-ISSN 1346-0447, Vol. 51, no 2, 167-173 p.Article in journal (Refereed) Published
##### Abstract [en]

It is proved that a Banach sequence lattice with the Fatou property and which is an AM space must be a weighted $\ell_{\infty}$ space (resp.\ a weighted $c_{0}$ space if it has an order continuous norm). Each symmetric (i.e.\ rearrangement invariant) Banach function space over a nonatomic $\sigma$-finite measure space with the Fatou property and which is an AM space must be a weighted $L_{\infty}$ space. Also some refinements in the absence of the Fatou property are obtained.

##### Place, publisher, year, edition, pages
2000. Vol. 51, no 2, 167-173 p.
Mathematics
##### Identifiers
Local ID: a95b6490-a574-11db-9811-000ea68e967bOAI: oai:DiVA.org:ltu-11578DiVA: diva2:984528
##### Note
Validerad; 2000; 20070112 (kani)Available from: 2016-09-29 Created: 2016-09-29Bibliographically approved

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Scientiae mathematicae Japonicae