Ditkin sets in homogeneous spaces
Volume 203 / 2011
Studia Mathematica 203 (2011), 291-307
MSC: Primary 43A85, 43A45; Secondary 46L07.
DOI: 10.4064/sm203-3-5
Abstract
Ditkin sets for the Fourier algebra $A(G/K),$ where $K$ is a compact subgroup of a locally compact group $G,$ are studied. The main results discussed are injection theorems, direct image theorems and the relation between Ditkin sets and operator Ditkin sets and, in the compact case, the inverse projection theorem for strong Ditkin sets and the relation between strong Ditkin sets for the Fourier algebra and the Varopoulos algebra. Results on unions of Ditkin sets and on tensor products are also given.
