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## Banach Center Publications

2010 | 91 | 1 | 339-351
Tytuł artykułu

### (Non-)amenability of ℬ(E)

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
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 $ℬ(E) = 𝒦(E) + ℂid_{E}$. Still, ℬ(ℓ²) is not amenable, and in the past decade, $ℬ(ℓ^{p})$ 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 $ℬ(ℓ^{p})$ for all p ∈ [1,∞].
Słowa kluczowe
Kategorie tematyczne
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Rocznik
Tom
Numer
Strony
339-351
Opis fizyczny
Daty
wydano
2010
Twórcy
autor
• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
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