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226. 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 $1 Categories:43A20, 46M20 227. CMB 1997 (vol 40 pp. 254) Saito, Kichi-Suke; Watatani, Yasuo  Subdiagonal algebras for subfactors II (finite dimensional case) We show that finite dimensional subfactors do not have subdiagonal algebras unless the Jones index is one. Categories:46K50, 46L37 228. CMB 1997 (vol 40 pp. 183) Kepert, Andrew G.  The range of group algebra homomorphisms A characterisation of the range of a homomorphism between two commutative group algebras is presented which implies, among other things, that this range is closed. The work relies mainly on the characterisation of such homomorphisms achieved by P.~J.~Cohen. Categories:43A22, 22B10, 46J99 229. CMB 1997 (vol 40 pp. 10) Borwein, Jon; Vanderwerff, Jon  Convex functions on Banach spaces not containing$\ell_1$There is a sizeable class of results precisely relating boundedness, convergence and differentiability properties of continuous convex functions on Banach spaces to whether or not the space contains an isomorphic copy of$\ell_1\$. In this note, we provide constructions showing that the main such results do not extend to natural broader classes of functions. Categories:46A55, 46B20, 52A41
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