On an inner product over Imc *-algebras

An inner product is defined on a commutative *-semisimple separable Frechet Q Imc *-algebra A and the resultant space Am is shown to be a topological *-algebra. It is also proved that every maximal ideal M of A is Am -closed and thus A can be decomposed into A = M + Mperpendicular. Further, it is shown that a norm can be defined on A which makes it into a pre C* -algebra. A completeness criterion for Am is established. (author). 10 refs