Extreme cases of weak type interpolation

Concerning weak ∗ - extreme points

Every separable nonreflexive Banach space admits an equivalent norm such that the set of the weak-extreme points of the unit ball is discrete.

Weak Interpolation in Banach Spaces

Interpolation by Weak Chebyshev Spaces

We present two characterizations of Lagrange interpolation sets for weak Chebyshev spaces. The rst of them is valid for an arbitrary weak Chebyshev space U and is based on an analysis of the structure of zero sets of functions in U extending Stockenberg's theorem. The second one holds for all weak Chebyshev spaces that possess a locally linearly independent basis. x1. Introduction Let U denote ...

Interpolation and Almost Interpolation by Weak Chebyshev Spaces

Some new results on univariate interpolation by weak Cheby-shev spaces, using conditions of Schoenberg-Whitney type and the concept of almost interpolation sets, are given. x1. Introduction Let U denote a nite-dimensional subspace of real-valued functions deened on some set K. We are interested in describing those conngurations T = dimU jT = s: T is called an interpolation set (I-set) w.r.t. U....

Restricted Weak Type versus Weak Type

We prove that translation invariant multilinear operators of restricted weak type (1, 1, . . . , 1, q) must necessarily be of weak type (1, 1, . . . , 1, q). We give applications.