Spectral theory for non-associative complete normed algebras and automatic continuity

This paper concerns normed algebras whose product is free of the requirement of associativity. For these algebras, a very natural notion of spectrum is provided and basic spectral properties of (associative) Banach algebras are extended to this general non-associative setting. These results are applied to generalize Rickart's dense-range homomorphism theorem. Our approach sheds some light on the classical associative theory.