Abstract
Abstract. Let A and B be complete normed algebras with a unit such that B is simple and power-associative, and let be a dense-range homomorphism. We prove that if θ is irreducible (that is, , for every closed proper ideal I of A), then θ is continuous. The continuity of non-irreducible homomorphisms is also obtained provided that the set of «spectrally rare »elements in the range algebra is not dense in B. These results extend the classical Rickart's dense-range homomorphism theorem to the non-associative setting.
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