On the Radius in Cayley-Dickson Algebras

TL;DR

This paper demonstrates that the radius in Cayley-Dickson algebras equals the Euclidean norm and explores related topics like Gelfand formula, subnorm stability, and functional power equations.

Contribution

It establishes that the radius in Cayley-Dickson algebras is given by the Euclidean norm, connecting algebraic and geometric properties.

Findings

Radius equals Euclidean norm in Cayley-Dickson algebras

Analysis of a variant of the Gelfand formula

Investigation of subnorm stability and functional power equations

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.