Obstacles to Bounded Recovery
نویسنده
چکیده
In this article, we are concerned with the following problem: let X be a Banach space, over the field F (F = C or R), V ⊂ X is an n-dimensional subspace of X and u1, . . . ,um are m linearly independent functionals on X. given x∈X we want to recover x on the basis of the values u1(x), . . . ,um(x)∈ F. Hence we are looking for a map F : X → V such that uj (Fx) = uj (x) for all j = 1, . . . ,m. Since we do not know x a priori we choose to look for a map F such that the norm of F
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