We study automatic injectivity of surjective algebra homomorphisms from B(X), the algebra of (bounded, linear) operators on X, to B(Y ), where X is one of the following long sequence spaces: c0(λ), c ∞ (λ), and p(λ) (1 p < ∞) and Y is arbitrary. En route to the proof that these spaces do indeed enjoy such a property, we classify two-sided ideals of the algebra of operators of any of the aforementioned Banach spaces that are closed with respect to the 'sequential strong operator topology'.