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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. https://resolver.caltech.edu/CaltechAUTHORS:20181003-155853311

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1006/jabr.1998.7849DOIArticle
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.
Funders:
Funding AgencyGrant Number
Technion100-013
Issue or Number:1
Record Number:CaltechAUTHORS:20181003-155853311
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181003-155853311
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, https://doi.org/10.1006/jabr.1998.7849. (http://www.sciencedirect.com/science/article/pii/S0021869398978498)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90107
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:06 Oct 2018 23:40
Last Modified:03 Oct 2019 20:22

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