This is an announcement for the paper "Uniform boundedness deciding sets, and a problem of M. Valdivia" by Olav Nygaard.

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.

Archive classification: math.FA

Remarks: 5 pages

Submitted from: olav.nygaard@uia.no

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1409.0102

or

http://arXiv.org/abs/1409.0102