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Search: MSC category 46M20 ( Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) [See also 14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx] )

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1. CMB 1997 (vol 40 pp. 133)

Blackmore, T. D.
Derivations from totally ordered semigroup algebras into their duals
For a well-behaved measure $\mu$, on a locally compact totally ordered set $X$, with continuous part $\mu_c$, we make $L^p(X,\mu_c)$ into a commutative Banach bimodule over the totally ordered semigroup algebra $L^p(X,\mu)$, 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 $L^p(X,\mu)$ into its dual module and in particular shows that if $\mu_c$ is not identically zero then $L^p(X,\mu)$ is not weakly amenable. We show that all bounded derivations from $L^1(X,\mu)$ into its dual module arise in this way and also describe all bounded derivations from $L^p(X,\mu)$ into its dual for $1
Categories:43A20, 46M20

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