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1998/1999 Monotone Norms on C(Ω) and Multiplicative Factors
Héctor H. Cuenya, Felipe Zó
Real Anal. Exchange 24(1): 215-222 (1998/1999).


Let $C(\Omega)$ be the algebra of continuous complex-valued functions on a topological space $\Omega$ and let $\rho$ be a function norm on $C(\Omega).$ We give necessary and sufficient conditions on the set $A_{\rho}=\{f\in C(\Omega)\:rho(f)<\infty\}$ to be an algebra. Also, we prove that every complete function norm is quasi-submultiplicative provided $A_{\rho}$ is an algebra and we give a characterization of the best multiplicative factor of $\rho.$ Finally we characterize the infinity norm and we prove that every quasi-submultiplicative function norm on $C(\Omega)$ is equivalent to the infinity norm.


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Héctor H. Cuenya. Felipe Zó. "Monotone Norms on C(Ω) and Multiplicative Factors." Real Anal. Exchange 24 (1) 215 - 222, 1998/1999.


Published: 1998/1999
First available in Project Euclid: 23 March 2011

zbMATH: 0945.46031
MathSciNet: MR1691747

Primary: 46H05 , 46J10

Keywords: algebra of continuous functions , monotone norms , multiplicative factors , submultiplicative norms

Rights: Copyright © 1998 Michigan State University Press

Vol.24 • No. 1 • 1998/1999
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