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
Bagarello, F., Trapani, C. (1996). Lp-spaces as quasi *-algebras. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 197(3), 810-824 [10.1006/jmaa.1996.0055].
Lp-spaces as quasi *-algebras
BAGARELLO, Fabio;TRAPANI, Camillo
1996-01-01
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
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