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Translation-finite sets and weakly compact derivations from l1(Z+) to its dual

Authors

Y. Choi, M. J. Heath*

* Corresponding author

Keywords

Status

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)

Reviews

[ Math Review (summary) | Zentralblatt ]

Abstract

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.

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Yemon Choi
Last modified: Thu Apr 7 18:58:33 CT 2011