L(P)-SPACES AS QUASI ASTERISK-ALGEBRAS

The Banach space L(p)(X,mu), for X a compact Hausdorff measure space, is considered as a special kind of quasi -algebra (called CQ*-algebra ) over the C-algebra C(X) of continuous functions on X. It is shown t hat, for p greater than or equal to 2, (L(p)(X, mu), C(X)) is -semisi mple (in a generalized sense). Some consequences of this fact are deri ved. (C) 1996 Academic Press, Inc.