Weak Chebyshev subspaces and alternation

Approximating weak Chebyshev subspaces by Chebyshev subspaces

We examine to what extent finite-dimensional spaces defined on locally compact subsets of the line and possessing various weak Chebyshev properties (involving sign changes, zeros, alternation of best approximations, and peak points) can be uniformly approximated by a sequence of spaces having related properties. r 2003 Elsevier Science (USA). All rights reserved.

WEAK CHEBYSHEV SUBSPACES AND , 4 - SUBSPACES OF C [ a , b ]

In this paper we show some very interesting properties of weak Chebyshev subspaces and use them to simplify Pinkus's characterization of Asubspaces of C[a, b]. As a consequence we obtain that if the metric projection PG from C[a, b] onto a finite-dimensional subspace G has a continuous selection and elements of G have no common zeros on (a, b), then G is an /4-subspace.

ε-weakly Chebyshev subspaces and quotient spaces

ε-weakly chebyshev subspaces and quotient 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 ...