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• # Artykuł - szczegóły

## Studia Mathematica

2007 | 179 | 2 | 149-166

## Second derivatives of norms and contractive complementation in vector-valued spaces

EN

### Abstrakty

EN
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 ∈ (1,2) ∪ (2,∞). 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 ∈ (1,2) ∪ (2,∞) and obtain a complete characterization of its 1-complemented subspaces.

149-166

wydano
2007

### Twórcy

autor
• Mathematics Institute, University of Warwick, CV4 7AL Coventry, United Kingdom
• Department of Mathematics and Statistics, Miami University, Oxford, OH 45056, U.S.A.
autor
• Mathematical Insitute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands