On one-complemented subspaces of Minkowski spaces with smooth Riesz norms

摘要

In this paper we study one-complemented subspaces of Minkowski spaces. The main objective is to examine norms on R-n for which every one-complemented subspace has a block basis, i.e., a basis of vectors with mutually disjoint supports. We introduce a collection of norms on R-n and show that, for these norms, each one-complemented subspace has a block basis. This collection contains, among others, finite sums of l(p)-norms, where 1 < p < infinity and p not equal 2, and their duals. In the proofs an important role is played by the derivative of the (scaled) duality map and, in particular, its behavior near the coordinate planes.