Sadahiro Saeki

On strong Ditkin sets

We shall regard the group algebra LI(G) as a closed ideal in M(G) (see [9, p. 16]). For a given closed subset E of F, let us denote by: I(E) = {f e L~(G) : f -= O on E}; Io(E ) {f e LI(G) : 0 on some neighborhood of E}; J(E) = the closure of I0(E), and, for any measure t ~ in M(G), define II/~ItE = sup {]If, #]1 : f e I0(E), I[fll -~ 1}. In other words, II#[IE is the operator norm of the mapping: f---->f,tt (from Io(E ) into LI(G)).