Uniform boundedness deciding sets, and a problem of M. Valdivia

Abstract

We prove that if a set $B$ in a Banach space $X$ can be written as an increasing, countable union $B={\cup }_n{B}_n$ of sets $B_n$ such that no $B_n$ is uniform boundedness deciding, then also $B$ is not uniform boundedness deciding. From this we can give a positive answer to a question of M. Valdivia.

The paper is withdrawn because there is a serious gap that I haven't been able to fill