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 = ∞. 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 ℓ¹, such that . Still, ℬ(ℓ²) is not amenable, and in the past decade, was found to be non-amenable for p = 1,2,∞ 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 for all p ∈ [1,∞].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-20,
author = {Volker Runde},
title = {(Non-)amenability of B(E)},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {339-351},
zbl = {1216.47109},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-20}
}
Volker Runde. (Non-)amenability of ℬ(E). Banach Center Publications, Tome 89 (2010) pp. 339-351. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-20/