Read produced the first example of a Banach space E such that the associated Banach algebra B(E) of bounded operators admits a discontinuous derivation (J. London Math. Soc. 1989). We generalize Read's main theorem about B(E) from which he deduced this conclusion, as well as the key technical lemmas that his proof relied on, by constructing a strongly split-exact sequence
{0}→W(E)→B(E)→l₂^~→{0},
W(E) where W(E) denotes the ideal of weakly compact operators on E, while l₂^~ is the unitization of the Hilbert space l₂, endowed with the zero product.