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Second derivatives of norms and contractive complementation in vector-valued spaces
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Lemmens, Bas, Randrianantoanina, Beata and van Gaans, Onno (2007) Second derivatives of norms and contractive complementation in vector-valued spaces. Studia Mathematica, Vol.179 (No.2). pp. 149-166. doi:10.4064/sm179-2-3 ISSN 0039-3223.
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Official URL: http://journals.impan.gov.pl/sm/
Abstract
We consider 1-complemented subspaces (ranges of contractive projections) of vector-valued spaces l(p)(X), where X is a Banach space with a 1-unconditional basis and p is an element of (1,2) boolean OR (2, infinity). If the norm of X is twice continuously differentiable and satisfies certain conditions connecting the norm and the notion of disjointness with respect to the basis, then we prove that every 1-complemented subspace of l(p)(X) admits a basis of mutually disjoint elements. Moreover, we show that every contractive projection is then an averaging operator. We apply our results to the space l(p)(l(q)) with p,q is an element of (1,2) boolean OR (2, infinity) and obtain a complete characterization of its 1-complemented subspaces.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Studia Mathematica | ||||
Publisher: | Polska Akademia Nauk | ||||
ISSN: | 0039-3223 | ||||
Official Date: | 2007 | ||||
Dates: |
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Volume: | Vol.179 | ||||
Number: | No.2 | ||||
Number of Pages: | 18 | ||||
Page Range: | pp. 149-166 | ||||
DOI: | 10.4064/sm179-2-3 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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