  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).
