Goldberg, Moshe and Luxemburg, W. A. J. (2004) Stable subnorms revisited. Pacific Journal of Mathematics, 215 (1). pp. 1527. ISSN 00308730. http://resolver.caltech.edu/CaltechAUTHORS:GOLpjm04

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Abstract
Let A be a finitedimensional, powerassociative algebra over a field F, either R or C, and let S, a subset of A, be closed under scalar multiplication. A realvalued 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 finitedimensional, powerassociative 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 100191. 
Record Number:  CaltechAUTHORS:GOLpjm04 
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:GOLpjm04 
Alternative URL:  http://pjm.math.berkeley.edu/2004/2151/p02.html 
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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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