Obstacles to bounded recovery

Abstract

Let $X$ be a Banach space, $V\subset X$ is its subspace and $U\subset X^{*}$. Given $x\in X$, we are looking for $v\in V$ such that $u\left(v\right)=u\left(x\right)$ for all $u\in U$ and $\Vert v\Vert \le M\Vert x\Vert$. In this article, we study the restrictions placed on the constant $M$ as a function of $X,V$, and $U$.