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- W1979078940 abstract "In 1972, the late B. E. Johnson introduced the notion of an amenable Banach algebra and asked whether the Banach algebra $B(E)$ of all bounded linear operators on a Banach space $E$ could ever be amenable if $dim E = infty$. Somewhat surprisingly, this question was answered positively only very recently as a by-product of the Argyros--Haydon result that solves the scalar plus compact problem: there is an infinite-dimensional Banach space $E$, the dual of which is $ell^1$, such that $B(E) = K(E)+ mathbb{C} id_E$. Still, $B(ell^2)$ is not amenable, and in the past decade, $ B(ell^p)$ was found to be non-amenable for $p=1,2,infty$ thanks to the work of C. J. Read, G. Pisier, and N. Ozawa. We survey those results, and then--based on joint work with M. Daws--outline a proof that establishes the non-amenability of $B(ell^p)$ for all $p in [1,infty]$." @default.
- W1979078940 created "2016-06-24" @default.
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- W1979078940 date "2009-09-14" @default.
- W1979078940 modified "2023-09-27" @default.
- W1979078940 title "(Non-)amenability of B(E)" @default.
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