Second derivatives of norms and contractive complementation in vector valued spaces

Lemmens, Bas and Van Gaans, Onno and Randrianantoanina, Beata (2007) Second derivatives of norms and contractive complementation in vector valued spaces. Studia Mathematica, 179 (2). pp. 149-166. ISSN 0039-3223. (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.4064/sm179-2-3

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: Article
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Divisions: Central Services
Depositing User: Bas Lemmens
Date Deposited: 17 Nov 2011 16:14
Last Modified: 11 Jan 2012 12:21
Resource URI: http://kar.kent.ac.uk/id/eprint/28443 (The current URI for this page, for reference purposes)
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