Lp-Spaces as Quasi *-Algebras

The Banach space Lp X,m., 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 that, for pG2, Lp X,m.,C X..is *-semisimple in a generalized sense.. Some consequences of this fact are derived.