Geodesic
Stable subnorms on finite-dimensional power-associative algebras
The electronic journal of linear algebra, Tome 17 (2008), pp. 359-375.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 on S is called a subnorm if $f(a)$ > 0 for all 0 = a $\in S$, and $f(\alpha a) = |\alpha |f(a)$ for all a $\in S$ and $\alpha \in F$. If in addition, S is closed under raising to powers, then a subnorm f is said to be stable if there exists a positive constant $\sigma $so that $f(a k ) \leq \sigma f(a)$ k for all a $\in S$ and k = 1, 2, 3, . . . .
Classification : 15A60, 16B99, 17A05
Keywords: finite-dimensional power-associative algebras, norms, subnorms, submoduli, stable subnorms, minimal polynomial, radius of an element in a finite-dimensional power-associative algebra 
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     author = {Goldberg, Moshe},
     title = {Stable subnorms on finite-dimensional power-associative algebras},
     journal = {The electronic journal of linear algebra},
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     volume = {17},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2008__17__a19/}
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Goldberg, Moshe. Stable subnorms on finite-dimensional power-associative algebras. The electronic journal of linear algebra, Tome 17 (2008), pp. 359-375. http://geodesic.mathdoc.fr/item/ELA_2008__17__a19/