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Non-amenability of 
${\mathcal {B}}(E)$ has been surprisingly difficult to prove for the classical Banach spaces, but is now known for E = ℓp and E = Lp for all 1 ⩽ p < ∞. However, the arguments are rather indirect: the proof for L1 goes via non-amenability of 
$\ell ^\infty ({\mathcal {K}}(\ell _1))$ and a transference principle developed by Daws and Runde (Studia Math., 2010).
In this note, we provide a short proof that 
${\mathcal {B}}(L_1)$ and some of its subalgebras are non-amenable, which completely bypasses all of this machinery. Our approach is based on classical properties of the ideal of representable operators on L1, and shows that 
${\mathcal {B}}(L_1)$ is not even approximately amenable.
We prove a quantized version of a theorem by M. V. Sheĭnberg: A uniform algebra equipped with its canonical, i.e., minimal, operator space structure is operator amenable if and only if it is a commutative 
${{C}^{*}}$-algebra.
