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.
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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.
|Subjects:||Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus|
|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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