Obstacles to bounded recovery

Abstract

Let X be a Banach space, V⊂X is its subspace and U⊂X*. Given x∈X, we are looking for v∈V such that u (v)=u (x) for all u∈U and ‖v‖ ≤M‖x‖. In this article, we study the restrictions placed on the constant M as a function of X,V, and U.