Geodesic
Derivations from Totally Ordered Semigroup Algebras into their Duals
Canadian mathematical bulletin, Tome 40 (1997) no. 2, pp. 133-142

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DOI

For a well-behaved measure μ, on a locally compact totally ordered set X, with continuous part μ c, we make Lp (X, μc ) into a commutative Banach bimodule over the totally ordered semigroup algebra Lp (X, μ), in such a way that the natural surjection from the algebra to the module is a bounded derivation. This gives rise to bounded derivations from Lp (X, μ) into its dual module and in particular shows that if μc is not identically zero then Lp (X, μ) is not weakly amenable. We show that all bounded derivations from L1 (X, μ) into its dual module arise in this way and also describe all bounded derivations from Lp(X, μ) into its dual for 1 < p < ∞ the case that X is compact and μ continuous.
DOI : 10.4153/CMB-1997-016-9
Mots-clés : 43A20, 46M20 
Blackmore, T. D. Derivations from Totally Ordered Semigroup Algebras into their Duals. Canadian mathematical bulletin, Tome 40 (1997) no. 2, pp. 133-142. doi: 10.4153/CMB-1997-016-9
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     title = {Derivations from {Totally} {Ordered} {Semigroup} {Algebras} into their {Duals}},
     journal = {Canadian mathematical bulletin},
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     year = {1997},
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     doi = {10.4153/CMB-1997-016-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-016-9/}
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