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Stable subnorms revisited

Goldberg, Moshe and Luxemburg, W. A. J. (2004) Stable subnorms revisited. Pacific Journal of Mathematics, 215 (1). pp. 15-27. ISSN 0030-8730. http://resolver.caltech.edu/CaltechAUTHORS:GOLpjm04

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Abstract

Let A be a finite-dimensional, power-associative algebra over a field F, either R or C, and let S, a subset of A, be closed under scalar multiplication. A real-valued function f defined on S, shall be called a subnorm if f(a) > 0 for all 0 not equal a is an element of S, and f(alpha a) = |alpha| f(a) for all a is an element of S and alpha is an element of F. If in addition, S is closed under raising to powers, then a subnorm f shall be called stable if there exists a constant sigma > 0 so that f(a(m)) less than or equal to sigma f(a)(m) for all a is an element of S and m = 1, 2, 3.... The purpose of this paper is to provide an updated account of our study of stable subnorms on subsets of finite-dimensional, power-associative algebras over F. Our goal is to review and extend several of our results in two previous papers, dealing mostly with continuous subnorms on closed sets.


Item Type:Article
Additional Information:© Copyright 2004 Pacific Journal of Mathematics. Received September 7, 2003. Research of the first author was sponsored in part by the Fund for the Promotion of Research at the Technion, Grant 100-191.
Record Number:CaltechAUTHORS:GOLpjm04
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:GOLpjm04
Alternative URL:http://pjm.math.berkeley.edu/2004/215-1/p02.html
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:593
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:01 Sep 2005
Last Modified:26 Dec 2012 08:40

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