Y. Choi, M. J. Heath*
* Corresponding author
Appeared as Bull. London Math. Soc. 42 (2010), no. 3, 429--440.
Preprint version available at arXiv 0811.4432 (last revised October 2009; revision posted March 2010)
[ Math Review (summary) | Zentralblatt ]
We characterize those derivations from the convolution algebra l1(Z+) to its dual which are weakly compact, providing explicit examples which are not compact. The characterization is combinatorial, in terms of ``translation-finite'' subsets of Z+, and we investigate how this notion relates to other notions of ``smallness'' for infinite subsets of Z+. In particular, we prove that a set of strictly positive Banach density cannot be translation-finite; the proof has a Ramsey-theoretic flavour.