On the radius in Cayley–Dickson algebras

Goldberg, Moshe; Laffey, Thomas

doi:10.1090/proc/12826

On the radius in Cayley–Dickson algebras
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by Moshe Goldberg and Thomas J. Laffey PDF

Proc. Amer. Math. Soc. 143 (2015), 4733-4744 Request permission

Abstract:

In the first two sections of this paper we provide a brief account of the Cayley–Dickson algebras and prove that the radius on these algebras is given by the Euclidean norm. With this observation we resort to three related topics: a variant of the Gelfand formula, stability of subnorms, and the functional power equation.

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http://en.wikipedia.org/wiki/Cayley-Dickson_construction
http://en.wikipedia.org/wiki/Sedenions