Abstract
Abstract: Araki and Elliott proved that if A is an associative complex *-algebra endowed with a complete vector space norm ∥ • ∥ such that ∥ a*a ∥ = ∥ a ∥2 for every a ∈ A , then the norm ∥ • ∥ is submultiplicative. In this paper we prove that the Araki–Elliott theorem remains true if 'associative' is relaxed to 'alternative'. We also prove that the Araki–Elliott theorem does not remain true if 'associative' is altogether removed.
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