| Affiliation: | Fachbereich Mathematik/Informatik, Universität Paderborn, D-33095 Paderborn, Germany ; Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 |
| Abstract: | Let  be a locally compact group,  the Fourier algebra of  and  the von Neumann algebra generated by the left regular representation of  . We introduce the notion of  -spectral set and  -Ditkin set when  is an  -invariant linear subspace of  , thus providing a unified approach to both spectral and Ditkin sets and their local variants. Among other things, we prove results on unions of  -spectral sets and  -Ditkin sets, and an injection theorem for  -spectral sets. |
