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Banach function lattices which are AM-spaces
Adam Mickiewicz University, Poznan.
LuleƄ University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0002-9584-4083
2000 (English)In: Scientiae mathematicae Japonicae, ISSN 1346-0862, E-ISSN 1346-0447, Vol. 51, no 2, p. 167-173Article 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, p. 167-173
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-11578Local ID: a95b6490-a574-11db-9811-000ea68e967bOAI: oai:DiVA.org:ltu-11578DiVA, id: diva2:984528
Note
Validerad; 2000; 20070112 (kani)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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  • de-DE
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Output format
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