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Read produced the first example of a Banach space $E_{\text{R}}$ such thatthe associated Banach algebra $\mathscr{B}(E_{\text{R}})$ of bounded operatorsadmits a discontinuous derivation (J. London Math. Soc. 1989). We generaliseRead's main theorem about $\mathscr{B}(E_{\text{R}})$ from which he deducedthis conclusion, as well as the key technical lemmas that his proof relied on,by constructing a strongly split-exact sequence {0} -->$\mathscr{W}(E_{\text{R}})$ --> $\mathscr{B}(E_{\text{R}})$-->$\tilde{\ell_2}$-->{0}, where $\mathscr{W}(E_{\text{R}})$ denotes the ideal ofweakly compact operators on $E_{\text{R}}$, while $\tilde{\ell_2}$ is theunitization of the Hilbert space $\ell_2$, endowed with the zero product.

Extensions and the weak Calkin algebra of Read's Banach space admitting discontinuous derivations