论文标题
简短的证明$ {\ Mathcal B}（L_1）$不适合
A short proof that ${\mathcal B}(L_1)$ is not amenable
论文作者
论文摘要
$ {\ Mathcal B}（e）$的不典型性在古典Banach空间中很难证明，但现在以$ e = \ ell_p $和$ e = l_p $而闻名，均为$ 1 \ leq P <\ leq p <\ infty $。但是，论点是间接的：$ l_1 $的证明是通过$ \ ell^\ infty（{\ Mathcal k}（\ ell_1））$进行的，而DAWS和Runde（Studia Math。，2010）开发的转移原则。在本说明中，我们提供了一个简短的证明，表明$ {\ Mathcal B}（L_1）$及其某些子代词不明，这完全绕开了所有这些机械。我们的方法基于$ L_1 $上代表运算符的理想的经典属性，并表明$ {\ Mathcal b}（L_1）$甚至都不可正约。
Non-amenability of ${\mathcal B}(E)$ has been surprisingly difficult to prove for the classical Banach spaces, but is now known for $E= \ell_p$ and $E=L_p$ for all $1\leq p<\infty$. However, the arguments are rather indirect: the proof for $L_1$ 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 $L_1$, and shows that ${\mathcal B}(L_1)$ is not even approximately amenable.
