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RESEARCH PRODUCT

Lp-Spaces as Quasi *-Algebras

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