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Abstrakty
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
Czasopismo
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
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-20