Automatic surjectivity of ring homomorphisms on H*-algebras and algebraic differences among some group algebras of compact groups

In this paper we present two automatic surjectivity results concerning ring homomorphisms between p-classes of an H*-algebra which, in some sense, imp rove the main theorem in a recent paper by the author (Proc. Amer. Math. So c. 124 (1996), 169-175) quite significantly. Furthermore, we apply our resu lts to show that for arbitrary infinite compact groups G; G', no quotient r ing of L-2 (G) is isomorphic to L-p (G') (2 < p less than or equal to infin ity), a statement we conjecture to be true for every pair L-p (G), L-q (G') of group rings corresponding to different exponents 1 less than or equal t o p, q less than or equal to infinity.