A singular, admissible extension which splits algebraically, but not   strongly, of the algebra of bounded operators on a Banach space
  Let $E$ be the Banach space constructed by Read (J. London Math. Soc. 1989) such that the Banach algebra $\mathscr{B}(E)$ of bounded operators on $E$ admits a discontinuous derivation. We show that $\mathscr{B}(E)$ 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, to appear). 
Tomasz Kania, Niels Jakob Laustsen and Richard Skillicorn
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