COMPLEMENTED IDEALS OF GROUP-ALGEBRAS

The existence of a projection onto an ideal I of a commutative group algebra L1(G) depends on its hull Z(I) subset-or-equal-to G. Existing methods for constructing a projection onto I rely on a decomposition of Z(I) into simpler hulls, which are then reassembled one at a time, resulting in a chain of projections which can be composed to give a projection onto I. These methods are refined and examples are constructed to show that this approach does not work in general. Some answers are also given to previously asked questions concerning such hulls and some conjectures are presented concerning the classification of these complemented ideals.