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We study automatic injectivity of surjective algebra homomorphisms from$\mathscr{B}(X)$, the algebra of (bounded, linear) operators on $X$, to$\mathscr{B}(Y)$, where $X$ is one of the following \emph{long} sequencespaces: $c_0(\lambda)$, $\ell_{\infty}^c(\lambda)$, and $\ell_p(\lambda)$ ($1\leqslant p < \infty$) and $Y$ is arbitrary. \textit{En route} to the proofthat these spaces do indeed enjoy such a property, we classify two-sided idealsof the algebra of operators of any of the aforementioned Banach spaces that areclosed with respect to the `sequential strong operator topology'.

Surjective homomorphisms from algebras of operators on long sequence spaces are automatically injective