A singular, admissible extension which splits algebraically, but not strongly, of the algebra of bounded operators on a Banach space

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• 作者：Tomasz Kania^a ; ¹ ; ^{tomasz.marcin.kania@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Niels Jakob Laustsen^b ; ^{n.laustsen@lancaster.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Richard Skillicorn^b ; ^{r.skillicorn@lancaster.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 46H40 ; 46M18 ; 47L10 ; secondary ; 16S70 ; 46B45 ; 46H10
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：15 November 2016
• 年：2016
• 卷：271
• 期：10
• 页码：2888-2898
• 全文大小：308 K

文摘

Let E be the Banach space constructed by Read [10] such that the Banach algebra B(E)$\mathcal{B}(E)$ of bounded operators on E   admits a discontinuous derivation. We show that B(E)$\mathcal{B}(E)$ has a singular, admissible extension which splits algebraically, but does not split strongly. This answers a natural question going back to the work of Bade, Dales, and Lykova [1], and complements recent results of Laustsen and Skillicorn [6].