This is an announcement for the paper "Some translation-invariant Banach function spaces which contain $c_0$" by Pascal Lefevre, Daniel Li, Herve Queffelec, and Luis Rodriguez-Piazza. Abstract: We produce several situations where some natural subspaces of classical Banach spaces of functions over a compact abelian group contain the space $c_0$. Archive classification: math.FA Mathematics Subject Classification: MSC: Primary: 43A46, 46B20; Secondary: 42A55, 42B35, 43A07, 46E30 Citation: Studia Mathematica 163, 2 (2004) 137 - 155 The source file(s), LLQR3D.TEX: 56689 bytes, is(are) stored in gzipped form as 0912.3133.gz with size 18kb. The corresponding postcript file has gzipped size 109kb. Submitted from: daniel.li@euler.univ-artois.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.3133 or http://arXiv.org/abs/0912.3133 or by email in unzipped form by transmitting an empty message with subject line uget 0912.3133 or in gzipped form by using subject line get 0912.3133 to: math@arXiv.org.