Complemented ideals in the Fourier algebra of a locally compact group. (English) Zbl 0928.46036
Summary: We provide a necessary condition for a closed ideal in the Fourier algebra of a locally compact amenable group to be completely complemented. The classification of completely complemented ideals is completed in the case of an amenable discrete group. We also investigate the ideals possessing a bounded approximate identity.
MSC:
| 46L07 | Operator spaces and completely bounded maps |
| 47L25 | Operator spaces (= matricially normed spaces) |
| 46J20 | Ideals, maximal ideals, boundaries |
| 43A30 | Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. |
| 46H25 | Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) |
