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On the radius in Cayley-Dickson algebras


Authors: Moshe Goldberg and Thomas J. Laffey
Journal: Proc. Amer. Math. Soc. 143 (2015), 4733-4744
MSC (2010): Primary 16P10, 17A05, 17A35, 17D05, 39B22
DOI: https://doi.org/10.1090/proc/12826
Published electronically: July 20, 2015
MathSciNet review: 3391032
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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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Additional Information

Moshe Goldberg
Affiliation: Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel
Email: mg@technion.ac.il

Thomas J. Laffey
Affiliation: School of Mathematical Sciences, University College Dublin, Dublin 4, Ireland
Email: thomas.laffey@ucd.ie

DOI: https://doi.org/10.1090/proc/12826
Keywords: Cayley--Dickson algebras, power-associative algebras, radius of an element in a finite-dimensional power-associative algebra, subnorms, the Gelfand formula, stability of subnorms, the power equation
Received by editor(s): April 3, 2015
Received by editor(s) in revised form: April 20, 2015
Published electronically: July 20, 2015
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2015 American Mathematical Society

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