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

Kania, Tomasz and Laustsen, Niels Jakob and Skillicorn, Richard (2016) A singular, admissible extension which splits algebraically, but not strongly, of the algebra of bounded operators on a Banach space. Journal of Functional Analysis, 271. pp. 2888-2898. ISSN 0022-1236

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Abstract

Let E be the Banach space constructed by Read (J. London Math. Soc. 1989) such that the Banach algebra B(E) of bounded operators on E admits a discontinuous derivation. We show that 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 (Mem. Amer. Math. Soc. 1999), and complements recent results of Laustsen and Skillicorn (C.R. Math. Acad. Sci. Paris 2016).