Lp-spaces as quasi *-algebras

Abstract

The Banach space Lp(X, μ), 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 p ≥ 2, (Lp(X, μ), C(X)) is *-semisimple (in a generalized sense). Some consequences of this fact are derived