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

This is a detailed study of the problem of the existence and character ization of finite-dimensional Chebyshev subspaces of the spaces phi(L) and L(p(t)) on the interval I = [-1, 1], where phi(t) is an even nonn egative continuous nondecreasing function on the half-fine [0, +infini ty) , and the function p(t) is measurable, finite, and positive almost everywhere on I. If phi is an N-function, it is characterized as a Ch ebyshev subspace of the Orlicz spaces with the Luxemburg norm.