$\mathcal {B}(\ell ^p)$ is never amenable

ug 2 00 9 B ( l p ) is never amenable

We show that, if E is a Banach space with a shrinking basis satisfying a certain condition, then the Banach algebra l∞(K(l2⊕E)) is not amenable; in particular, this is true for E = l with p ∈ (1,∞). As a consequence, l∞(K(E)) is not amenable for any infinite-dimensional Lp-space. This, in turn, entails the non-amenability of B(lp(E)) for any Lp-space E, so that, in particular, B(lp) and B(Lp[0,...

B(ℓ p ) can never be amenable

We show that, if E is a Banach space with a basis satisfying a certain condition, then the Banach algebra l∞(K(l2 ⊕ E)) is not amenable; in particular, this is true for E = l with p ∈ (1,∞). As a consequence, l∞(K(E)) is not amenable for any infinite-dimensional Lp-space. This, in turn, entails the non-amenability of B(lp(E)) for any Lp-space E, so that, in particular, B(lp) and B(Lp[0, 1]) are...

P-Amenable Locally Compact Hypergroups

p-amenable locally compact hypergroups

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Inheritance of Convexity for the $\mathcal{P}_{\min}$-Restricted Game

We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the subcomponents corresponding to a minimum partition. This minimum partition Pmin is induced by the deletion of the minimum weight edges. We provide a characterization of the graphs satisfying inherita...