B(ℓ p ) can never be amenable
نویسنده
چکیده
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 not amenable.
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