(Non-)amenability of B(E)
نویسنده
چکیده
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 dimE = ∞. 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 infinitedimensional Banach space E, the dual of which is l, such that B(E) = K(E)+C idE . Still, B(l2) is not amenable, and in the past decade, B(lp) was found to be nonamenable 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 B(lp) for all p ∈ [1,∞].
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