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

• Autorzy: Bas Lemmens , Beata Randrianantoanina , Onno van Gaans
• Języki publikacji: 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.

Kategorie tematyczne

• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 46B04: Isometric theory of Banach spaces
• 46B45: Banach sequence spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 179
• Numer: 2
• Strony: 149-166

Daty

wydano

2007

Twórcy

autor

Bas Lemmens

• Mathematics Institute, University of Warwick, CV4 7AL Coventry, United Kingdom

autor

Beata Randrianantoanina

• Department of Mathematics and Statistics, Miami University, Oxford, OH 45056, U.S.A.

autor

Onno van Gaans

• Mathematical Insitute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands

Identyfikatory

DOI

10.4064/sm179-2-3