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Stable Norms on Complex Numbers and Quaternions

Arens, Richard and Goldberg, Moshe and Luxemburg, W. A. J. (1999) Stable Norms on Complex Numbers and Quaternions. Journal of Algebra, 219 (1). pp. 1-15. ISSN 0021-8693. doi:10.1006/jabr.1998.7849.

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In this paper, we study stability properties of norms on the complex numbers and on the quaternions. Our main findings are that these norms are stable if and only if they majorize the modulus function and that not all stable norms are strongly stable. Part of the paper is devoted to the standard matrix representations of the above number systems, where we show that norms on the corresponding matrix algebras are stable if and only if they are spectrally dominant. We conclude by considering proper seminorms, observing that none are stable on the complex numbers or on the quaternions.

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Additional Information:© 1999 Academic Press. Under an Elsevier user license. Received 9 September 1998. Communicated by Efim Zelmanov. Research sponsored in part by the Fund for the Promotion of Research at the Technion, Grant 100-013.
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Issue or Number:1
Record Number:CaltechAUTHORS:20181003-155853311
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Official Citation:Richard Arens, Moshe Goldberg, W.A.J Luxemburg, Stable Norms on Complex Numbers and Quaternions, Journal of Algebra, Volume 219, Issue 1, 1999, Pages 1-15, ISSN 0021-8693, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90107
Deposited By: George Porter
Deposited On:06 Oct 2018 23:40
Last Modified:16 Nov 2021 00:40

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