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Subspaces of l(infinity)(Gamma) without quasicomplements
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
2002 (English)In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 130, 281-283 p.Article in journal (Refereed) Published
Abstract [en]

J. Lindenstrauss proves in [L] that c(0)(Gamma) is not quasicomplemented in L-infinity(Gamma) while H. P. Rosenthal in [R] proves that subspaces, whose dual balls are weak* sequentially compact and weak* separable, are quasicomplemented in l(infinity)(Gamma). In this note it is proved that weak* separability of the dual is the precise condition determining whether a subspace, without isomorphic copies of l(1) and whose dual balls are weak* sequentially compact, is quasicomplemented or not in l(infinity)(Gamma). Especially spaces isomorphic to l(p)(Gamma), for 1 < p < infinity, have no quasicomplements in l(infinity)(Gamma) if Gamma is uncountable.

Place, publisher, year, edition, pages
2002. Vol. 130, 281-283 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-48786OAI: oai:DiVA.org:liu-48786DiVA: diva2:269682
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-12

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