ON FINITE-DIMENSIONAL CHEBYSHEV SUBSPACES OF SPACES WITH AN INTEGRAL METRIC

Abstract

This is a detailed study of the problem of the existence and characterization of finite-dimensional Chebyshev subspaces of the spaces and on the interval , where is an even nonnegative continuous nondecreasing function on the half-line , and the function is measurable, finite, and positive almost everywhere on . If is an -function, it is characterized as a Chebyshev subspace of the Orlicz spaces with the Luxemburg norm.