Here is my question; I appreciate any and all help and hints.

We assume that A is a finite dimensional linear subspace of the normed linear space C[0,1] of continuous functions on the interval [0,1]. We let f be in C[0,1] and define a(p) to be the best approximation from A to f as defined by the p norm for functions. We define a* to be the best approximation from A to f as defined by the Chebyshev norm. Does the sequence   {a(1),a(2),...} of best approximations to f in Lp converge to a* as [LaTeX ERROR: Convert failed] approaches infinity?


Best Regards, Dmitro.