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 [10] such that the Banach algebra B(E)B(E) of bounded operators on E   admits a discontinuous derivation. We show that B(E)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].