Finite dimensional Chebyshev subspaces Of ℓ∞

Abstract EN

If A is a subset of the normed linear space X, then A is said to be proximinal in X if for each xX there is a point y0A such that the distance between x and A; d(x, A) = inf{||xy||: yA}= ||xy0||.

The element y0 is called a best approximation for x from A.

If for each xX, the best approximation for x from A is unique then the subset A is called a Chebyshev subset of X.

In this paper the author studies the existence of finite dimensional Chebyshev subspaces of